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  • A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction of the heat energy is converted into work?<strong

A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction of the heat energy is converted into work?

Option: 1

1


Option: 2

\frac{2}{3}


Option: 3

\frac{2}{5}


Option: 4

\frac{5}{7}


Answers (1)

best_answer

Heat energy supplied \mathrm{d Q=C_p d T}. Change in internal energy \mathrm{d U=C_v d T}. Therefore,

\mathrm{\text { work done } d W=d Q-d U=\left(C_p-C_v\right) d T}

\mathrm{\begin{aligned} & \therefore \frac{d W}{d Q}=\frac{\left(C_p-C_v\right) d T}{C_p d T}=1-\frac{1}{\gamma} \\ & =1-\frac{1}{5 / 3}=\frac{2}{5} \end{aligned}}

\mathrm{(\because \gamma=5 / 3 \text { for a monoatomic gas) }}

Posted by

Rishabh

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