Question

When an ideal diatomic gas is heated at constant pressure , the fraction of heat energy supplies which is used in doing work to maintain pressure constant is:

• A. 5/7
• B. 7/2
• C. 2/7
• D. 2/5

Answer 1

The correct option is A 5/7

Fraction of heat energy supplied which increases the internal energy

We know that,

Number of moles the gas $=n$

Specific heat at constant volume $=c_v$

Specific heat at constant pressure $=c_p$

Change in temperature $=dT$

Ratio of specific heats of gas $=\gamma$

Now,

$\frac{\Delta U}{\Delta Q}=\frac{n{c}_{v}dT}{n{c}_{p}dT}$

$\frac{\Delta U}{\Delta Q}=\frac{c_v}{c_p}$

$\frac{\Delta U}{\Delta Q}=\frac{1}{\gamma }$

For diatomic gas $\gamma =\frac{7}{5}$

So,

$\frac{\Delta U}{\Delta Q}=\frac{1}{\gamma }$

$\frac{\Delta U}{\Delta Q}=\frac{5}{7}$

The fraction of heat energy supplied is $\frac{5}{7}$.