Question

The molar heat capacity of a gas in a process

• A. is either $C_{V}$ or $C_{P}$
• B. lies between $C_{V}$ or $C_{P}$
• C. may range from zero to infinity
• D. can have any real value

Answer 1

Answer: (D)

Since $\Delta Q=\Delta U+\Delta W$, from first law of thermodynamics,
$\therefore $ The molar heat capacity $C$ is given by
$C=\frac{\Delta Q}{n \Delta T}=\frac{\Delta U+\Delta W}{n \Delta T}$
Assuming $\Delta T$ to be positive, $C>=<0$,
accordingly as, $\Delta U >=<-\Delta W$
i.e., $C$ can be positive, zero or negative.
Further, as $\Delta T>\rightarrow 0, C \rightarrow \pm \infty$
and as $\Delta T \rightarrow \infty, C \rightarrow 0$
In other words, $C$ can have any real value, depending upon the type of thermodynamic process.