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: Understanding the Concept
At constant pressure, heat supplied \(Q=nC_{p}\Delta T\) and work done \(W=nR\Delta T\).

Step 2: Fraction as work
\(\dfrac{W}{Q}=\dfrac{R}{C_{p}}=\dfrac{\gamma-1}{\gamma}\)

Step 3: Calculation
With \(\gamma=\frac{3}{2}\): \(\dfrac{3/2-1}{3/2}=\dfrac{1/2}{3/2}=\dfrac{1}{3}\approx33\%\)

Final Answer:
About 33 percent of the heat goes into external work. \[ \boxed{\text{(C) }33\ \%} \]