Question

A monatomic gas expands at constant pressure on heating. The percentage of heat supplied that increases the internal energy of the gas and that is involved in the expansion is

• A. $75\%$, $25\%$
• B. $25\%$, $75\%$
• C. $60\%$, $40\%$
• D. $40\%$, $60\%$

Answer 1

The correct option is C $60\%$, $40\%$

According to the first law of thermodynamics,
Q = U + W
Now, at constant pressure,
W = $P\Delta V=nR\Delta T$
U = $n{C}_v\Delta T$
For, a monoatomic gas, $C_v=1.5R$

Thus, $Q=n{C}_p\Delta T=2.5nR\Delta T$ $C_p=C_v+R$

Now, $\frac{U}{Q}=\frac{1.5R}{2.5R}$ = 60 %

Similarly, $\frac{W}{Q}=\frac{R}{2.5R}$ = 40 %