Question

When an ideal gas $(\gamma =\frac{5}{3})$ is heated under constant pressure, what percentage of given heat energy will be utilized in doing external work?

• A. $40\%$
• B. $30\%$
• C. $60\%$
• D. $20\%$

Answer 1

The correct option is A $40\%$

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