Question

When a diatomic gas expands at constant pressure, the percentage of heat supplied that increases temperature of the gas and in doing external work in expansion at constant pressure is:

• A. 60%
• B. 40%
• C. 28.57 %
• D. 71.42 %

Answer 1

The correct option is A 60%

We know that,

For an isobaric process

$Q=n{c}_p\Delta T$

$W=nR\Delta T$

Now,

$c_p=\frac{\gamma R}{\gamma -1}$

Now,

$\frac{\Delta W}{\Delta Q}=\frac{nR\Delta T}{n{c}_p\Delta T}$

$\frac{\Delta W}{\Delta Q}=\frac{R}{c_p}$

$\frac{\Delta W}{\Delta Q}=\frac{\gamma -1}{\gamma }$

For diatomic gas $\gamma =\frac{5}{2}$

Now,

$\frac{\Delta W}{\Delta Q}=\frac{\frac{5}{2}-1}{\frac{5}{2}}$

$\frac{\Delta W}{\Delta Q}=\frac{3}{5}$

$\frac{\Delta W}{\Delta Q}=0.6$

$\frac{\Delta W}{\Delta Q}\times 100=60$

Hence, this is required solution