A monoatomic gas performs work W=Q/4, where Q is the heat supplied to it. If the molar heat capacity during this transformation is C=xR, find x.
Physics · Thermodynamics
JEE Mains 2022

Question

A monoatomic gas performs work W=Q/4, where Q is the heat supplied to it. If the molar heat capacity during this transformation is C=xR, find x.

G1 Physics · Accepted Answer

From the first law, ΔU=Q−W=3Q/4. For one mole of a monoatomic gas, ΔU=(3/2)RΔT. Hence Q=2RΔT, so the molar heat capacity C=Q/ΔT=2R. Therefore x=2.