KVPY Sample Paper KVPY Stream-SX Model Paper-2

A certain mass of gas undergoes a process given by \[dU=\frac{dW}{2}.\] If the molar heat capacity of the gas for this process is \[\frac{15}{2}R,\] then the gas is:

A) Monoatomic

B) polyatomic

C) Diatomic

D) data insufficient

Correct Answer: C

Solution :

[C]

\[dU=\frac{dW}{2}\]

By 1st law \[\to dQ=3dU=3n{{C}_{\text{v}}}dT\]

Molar heat capacity \[C=\frac{dQ}{ndT}=3{{C}_{\text{v}}}\]

Given \[C=\frac{15R}{2}\]

\[\therefore {{C}_{\text{v}}}=\frac{5}{2}R\]

\[\therefore \]Degree of freedom =5

so gas is diatomic.