An ideal gas follows a process described by the equation PV² = C from the initial (P₁, V₁, T₁) to final (P₂, V₂, T₂) thermodynamic states, where C is a constant. Then (a) If P₁ > P₂ then V₁ > V₂ (b) If P₁ > P₂ then T₁ V₁ then T₂ > T₁ (d) If V₂ > V₁ then T₂ < T₁

Answer: (d). PV² = C and PV = nRT give T = PV/nR = C/nRV, so T ∝ 1/V. Also P ∝ 1/V²: if P₁ > P₂ then V₁ T₂, so (b) is false. If V₂ > V₁ then T₂ < T₁, so (c) is false and (d) is true. So the answer is (d).

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Thermodynamic Processes

An ideal gas follows a process described by the equation $PV^{2} = C$ from the initial $(P_1, V_1, T_1)$ to final $(P_2, V_2, T_2)$ thermodynamic states, where C is a constant. Then

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Answer: (d)

$PV^2 = C$ and $PV = nRT$ give $T = \frac{PV}{nR} = \frac{C}{nRV}$ , so $T \propto \frac{1}{V}$ .
Also $P \propto \frac{1}{V^2}$ : if $P_1 > P_2$ then $V_1 < V_2$ , so (a) is false, and then $T_1 > T_2$ , so (b) is false.
If $V_2 > V_1$ then $T_2 < T_1$ , so (c) is false and (d) is true.
So the answer is (d).

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