Question:
A gas for which \(\gamma =5/3\ (\gamma =C_{p}/C_{v})\) is heated at constant pressure. The percentage of heat supplied used for external work is
A gas for which \(\gamma =5/3\ (\gamma =C_{p}/C_{v})\) is heated at constant pressure. The percentage of heat supplied used for external work is
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The fraction of heat converted into work at constant pressure is R divided by Cp, which equals (gamma - 1) over gamma.
Updated On: Nov 12, 2026
- \(20\ \%\)
- \(40\ \%\)
- \(60\ \%\)
- \(80\ \%\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
At constant pressure, heat supplied \(Q=nC_p\Delta T\) and external work \(W=nR\Delta T\).
Step 2: Fraction used as work
\(\dfrac{W}{Q}=\dfrac{R}{C_p}=\dfrac{C_p-C_v}{C_p}=1-\dfrac{1}{\gamma}\)
Step 3: Substitute
With \(\gamma=\dfrac{5}{3}\): \(\dfrac{W}{Q}=1-\dfrac{3}{5}=\dfrac{2}{5}=40\%\).
Final Answer:
40 percent of the heat supplied is used for external work. \[ \boxed{\text{(B) }40\ \%} \]
At constant pressure, heat supplied \(Q=nC_p\Delta T\) and external work \(W=nR\Delta T\).
Step 2: Fraction used as work
\(\dfrac{W}{Q}=\dfrac{R}{C_p}=\dfrac{C_p-C_v}{C_p}=1-\dfrac{1}{\gamma}\)
Step 3: Substitute
With \(\gamma=\dfrac{5}{3}\): \(\dfrac{W}{Q}=1-\dfrac{3}{5}=\dfrac{2}{5}=40\%\).
Final Answer:
40 percent of the heat supplied is used for external work. \[ \boxed{\text{(B) }40\ \%} \]
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