Question

The molar heat capacity for an ideal gas

• A. is zero for an adiabatic process
• B. is infinite for an isothermal process
• C. depends only on the nature of the gas for a process in which either volume or pressure is constant
• D. is equal to the product of the molecular weight and specific heat capacity for any process

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A is zero for an adiabatic process
B is infinite for an isothermal process
C depends only on the nature of the gas for a process in which either volume or pressure is constant
D is equal to the product of the molecular weight and specific heat capacity for any process

By definition,$dQ=nCdT$, $C$=molar heat capacity, $n$=number of moles,
For adiabatic process, $dQ=0\Rightarrow C=0$
For isotherm, $dT=0\Rightarrow forfinitedQ,C=infinite$
For constant volume and pressure, $C=C_v$ and $C=C_p$ respectively which depend on atomicity of gas undergoing the process.

Again by definition $dQ=mcdT$, $m$=mass, $c$=specific heat
$\Rightarrow nC=mc$
$C=mc/n=Mc$, where $M$=molecular weight

Hence all options are correct