1. Tardigrade
  2. Question
  3. Physics
  4. One mole of an ideal gas has internal energy given by U=U0+2PV , where P is the pressure and V is the volume of the gas. U0 is a constant. This gas undergoes the quasi-static cyclic process ABCD as shown in the U-V diagram <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-pusfukyzzyd28zzc.jpg /> The molar heat capacity of the gas at constant pressure is

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Q. One mole of an ideal gas has internal energy given by $U=U_{0}+2PV$ , where $P$ is the pressure and $V$ is the volume of the gas. $U_{0}$ is a constant. This gas undergoes the quasi-static cyclic process $ABCD$ as shown in the $U-V$ diagram
Question
The molar heat capacity of the gas at constant pressure is

NTA AbhyasNTA Abhyas 2022

Solution:

Given relation for internal energy is $U=U_{0}+2PV$ .
For this cyclic process change in internal energy is given by
$\Delta U=2\Delta \left(P V\right)=2R\Delta T$
$\Rightarrow C_{V}=2R$
$\Rightarrow C_{p}=C_{V}+R=3R$