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The-molar-heat-capacity-of-a-metal-at-low-temperature-varies-with-the-temperature-according-to-the-equation-C-b-a-H-3-where-a-b-and-H-are-constant-How-much-heat-per-mole-is-transfe




Question Number 58216 by Umar last updated on 20/Apr/19
The molar heat capacity of a metal  at  low temperature varies with the   temperature according to the equation         C = bθ + (a/H)θ^3   where a, b and H are constant.  How much heat per mole is transfered  during the process in which the   temperature change from 0.01H   to 0.02H ?
ThemolarheatcapacityofametalatlowtemperaturevarieswiththetemperatureaccordingtotheequationC=bθ+aHθ3wherea,bandHareconstant.Howmuchheatpermoleistransferedduringtheprocessinwhichthetemperaturechangefrom0.01Hto0.02H?
Commented by Umar last updated on 20/Apr/19
please help!
pleasehelp!
Answered by tanmay last updated on 20/Apr/19
it is a question of chemistry...  however can be solved...  C_(molar) =(dQ/n)→dQ=heat ,n=nos of mole,C_(molar)  =molar heat  capacity.here n=1mole  i have doubt of unit of temparatue  change from0.01H to 0.02H (as per question)  what is H...  C_(molar=) =(dQ/n)  dQ=1×C  Q=∫_θ_i  ^θ_f   1×(bθ+(a/H)θ^3 )dθ  =∣((bθ^2 )/2)+(a/H)×(θ^4 /4)∣_θ_i  ^θ_r    =(b/2)(θ_f ^2 −θ_i ^2 )+(a/(4H))(θ_f ^4 −θ_i ^4 )  =(b/2){(0.02)^2 −(0.01)^2 }+(a/(4H)){(0.02)^4 −(0.01)}
itisaquestionofchemistryhowevercanbesolvedCmolar=dQndQ=heat,n=nosofmole,Cmolar=molarheatcapacity.heren=1moleihavedoubtofunitoftemparatuechangefrom0.01Hto0.02H(asperquestion)whatisHCmolar==dQndQ=1×CQ=θiθf1×(bθ+aHθ3)dθ=∣bθ22+aH×θ44θiθr=b2(θf2θi2)+a4H(θf4θi4)=b2{(0.02)2(0.01)2}+a4H{(0.02)4(0.01)}
Commented by Umar last updated on 20/Apr/19
thank you so much  i doughted the unit of temp too
thankyousomuchidoughtedtheunitoftemptoo
Commented by tanmay last updated on 20/Apr/19
most welcome...
mostwelcome

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