Question

A gas for which \(\gamma\) is \(3/2\) is heated at constant pressure. The percentage of heat supplied for external work is nearly

• A. \(11\ \%\)
• B. \(22\ \%\)
• C. \(33\ \%\)
• D. \(44\ \%\)

Hint:

At constant pressure the fraction of heat converted to work is the gas constant divided by the molar heat capacity at constant pressure, which equals (gamma minus 1) divided by gamma.

Answer 1

The Correct Option is C

Step 1: Using Cp and Cv
$C_{p}-C_{v}=R$ and $\dfrac{C_{p}}{C_{v}}=\dfrac{3}{2}$, so $C_{p}=3R$ and $C_{v}=2R$.

Step 2: Calculation
$\dfrac{W}{Q}=\dfrac{R}{3R}=\dfrac{1}{3}$, which is about $33\%$.

Step 3: Final answer
The work fraction is one-third, about 33 percent.

Final Answer:
The work fraction is one-third, about 33 percent. \[ \boxed{\text{(C) }33\ \%} \]