Question

In an isobaric process of an ideal gas. The ratio of heat supplied and work done by the system $\left[ie,\left(\frac{Q}{W}\right)\right]$ is

• A. $\frac{\gamma -1}{\gamma }$
• B. $\gamma$
• C. $\frac{\gamma }{\gamma -1}$
• D. $1$

Answer 1

Answer: (C)

From ideal gas equation
$pV=nRT$...(i)
where, $p$ is pressure,
$V$ the volume,
$R$ the gas constant,
$T$ the absolute temperature.
For isobaric process
$Q=n{C}_p\Delta T$...(ii)
$W=p\Delta V$...(iii)
where, $C_p$ is specific heat at constant pressure.
From Eqs. (i), (ii) and (iii), we get
$\frac{Q}{W}=\frac{n{C}_p\Delta T}{nR\Delta T}$
$=\frac{C_p}{R}$
$=\frac{\gamma }{\gamma -1}$