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  • The molar heat capacity in a process of a diatomic gas if it does a work of  , when <

The molar heat capacity in a process of a diatomic gas if it does a work of  \mathrm{Q / 4}, when \mathrm{Q } amount of heat is supplied to it is
 

Option: 1

\frac{2}{5} \mathrm{R}

 


Option: 2

\frac{5}{2} \mathrm{R}
 


Option: 3

\frac{10}{3} \mathrm{R}
 


Option: 4

\frac{6}{7} \mathrm{R}


Answers (1)

best_answer

\mathrm{\quad \mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}=\left(\frac{5}{2} \mathrm{R}\right) \mathrm{dT} \Rightarrow \mathrm{dT}=\frac{2(\mathrm{dU})}{5 \mathrm{R}}}
From 1^{\text {st }} law of thermodynamics \mathrm{d U=d Q-d W \: or\: d U=Q-\frac{Q}{4}=\frac{3 Q}{4}}

Now molar heat capacity \mathrm{\mathrm{C}=\frac{\mathrm{dQ}}{\mathrm{dT}}=\frac{\mathrm{Q}}{2\left(\frac{\mathrm{dU}}{5 \mathrm{R}}\right)}=\frac{5 \mathrm{QR}}{2\left(\frac{3 \mathrm{Q}}{4}\right)}=\frac{10}{3} \mathrm{R}}
 

Posted by

jitender.kumar

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