Question

A certain amount of an ideal monatomic gas needs 20 J of heat energy to raise its temperature by ${10}^{0}C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be :

• A. 30 J
• B. 12 J
• C. 200 J
• D. 215.3 J

Answer 1

The correct option is B 12 J

Since the gas is monoatomic

$\Rightarrow C_v=\frac{3R}{2}$

and $C_p=\frac{5R}{2}$

Now,

Let the no of moles of has $=n$ moles

We know that,

at constant pressure

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

$\Rightarrow 20=n\times \frac{5R}{2}\times 10$

$\Rightarrow n=\frac{4}{5R}$

and, at constant volume

$\Delta Q=n{C}_v\Delta T$

putting the values of $n$ and $\Delta T,C_v$

$\Delta Q=\frac{4}{5R}\times \frac{3R}{2}\times 10$

$\Rightarrow \Delta Q=12J$