Question

A monoatomic gas expands at a 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 D $40\%,60\%$

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 = $2.5nR\Delta T$
Now, $\frac{U}{Q}=\frac{1.5R}{2.5R}=60\%$
Similarly, $\frac{W}{Q}=\frac{R}{2.5R}=40\%$