Question 950: Thermodynamics & KTG

Question

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

Accepted Answer

Heat supplied at constant pressure $$\mathrm{Q_1}=\mathrm{nC}_{\mathrm{p}} \mathrm{dT}$$
Heat supplied at constant volume $$\mathrm{Q_2}=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}$$
Work done
$$\begin{aligned}
& \mathrm{W}=\mathrm{Q}_1-\mathrm{Q}_2=\mathrm{n}\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}ight) \mathrm{dT} \
& 	herefore \frac{\mathrm{W}}{\mathrm{Q}_2}=\frac{\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}}{\mathrm{C}_{\mathrm{v}}}=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}-1=\frac{5}{3}-1=\frac{2}{3} \
& 	herefore \mathrm{Q}_2=\frac{3 \mathrm{~W}}{2}
\end{aligned}$$

Answer

W

Answer

$$\mathrm{\frac{5W}{2}}$$

Answer

$$\mathrm{\frac{W}{2}}$$

Answer

$$\mathrm{\frac{3W}{2}}$$

Thermodynamics & KTG

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

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