Question

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

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

Answer 1

Answer: (C)

From ideal gas equation
$p V=n R T$...(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
$\frac{Q}{W} =\frac{n C_{p} \Delta T}{n R \Delta T}$
$=\frac{C_{p}}{R}$
$=\frac{\gamma}{\gamma-1}$