Question 651: Thermodynamics & KTG

Question

A sample of an ideal gas $\left(\gamma=\frac{5}{3}\right)$ is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

Accepted Answer

For constant pressure,
Using first law of thermodynamics,
$$ \begin{aligned} & \mathrm{W}=\mathrm{Q}-\Delta \mathrm{U} \ & \mathrm{~W}=\mathrm{mC}_{\mathrm{p}} \Delta \mathrm{~T}-\mathrm{mC}_{\mathrm{v}} \Delta \mathrm{~T} \end{aligned} $$
For monoatomic gas $\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}$
$$ \begin{array}{ll} \Rightarrow & C_v=\frac{3}{5} C_p \ 	herefore & W=m C_p \Delta T-m\left(\frac{3}{5} C_pight) \Delta T \ 	herefore & W=\frac{2}{5} m C_p \Delta T=\frac{2}{5} 	imes Q \Rightarrow W=\frac{2}{5} 	imes 100 \ 	herefore & W=40 J \end{array} $$

Answer

150 J

Answer

60 J

Answer

40 J

Answer

250 J

Thermodynamics & KTG

A sample of an ideal gas \left(\gamma=\frac{5}{3}\right) is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

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