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 ?
Answer & explanation
Correct answer: option 1
\(\frac{\Delta W}{\Delta Q} = \frac{\Delta Q - \Delta U}{\Delta Q}\)
\(\frac{\Delta W}{\Delta Q} = \frac{C_P - C_V}{C_P}\)
\(\frac{\Delta W}{\Delta Q} = 1 - \frac{1}{\gamma}\)
\(\frac{\Delta W}{\Delta Q} = 1 - \frac{1}{1 - \frac{5}{3}}\)
\(\frac{\Delta W}{\Delta Q} = \frac{2}{5}\)
i.e. percentage energy utilized in doing external work = \(\frac{2}{5}\) x 100 = 40%