(D) Given the condition $VP^2 = \text{constant}$.From the ideal gas equation, $PV = nRT$, so $V = nRT/P$.Substituting $V$ into the given condition: $(

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(D) Given the condition $VP^2 = \text{constant}$.From the ideal gas equation, $PV = nRT$, so $V = nRT/P$.Substituting $V$ into the given condition: $(nRT/P) \cdot P^2 = \text{constant} \implies TP = \text{constant}$.Thus, $P \propto 1/T$, which represents a rectangular hyperbola on a $P-T$ diagram.Since $VP^2 = \text{constant}$, we have $P^2 \propto 1/V$, which means $P \propto 1/\sqrt{V}$.If the volume $V$ becomes $4V$, then the new pressure $P'$ is $P' \propto 1/\sqrt{4V} = (1/2) \cdot (1/\sqrt{V}) = P/2$.Therefore, both statements $(A)$ and $(B)$ are correct.

Class 11 Physics Thermodynamics Polytropic Process

During an experiment, an ideal gas is found to obey a condition $VP^2 = \text{constant}$. The gas is initially at a temperature $T$, pressure $P$, and volume $V$. The gas expands to volume $4V$. Which of the following statements is correct?

A
The pressure of the gas changes to $P/2$.
B
The graph of the above process on the $P-T$ diagram is a hyperbola.
C
The graph of the above process on the $P-T$ diagram is a parabola.
D
Both $(A)$ and $(B)$.

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During an experiment, an ideal gas is found to obey a condition $VP^2 = \text{constant}$. The gas is initially at a temperature $T$, pressure $P$, and volume $V$. The gas expands to volume $4V$. Which of the following statements is correct?

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An ideal gas with heat capacity at constant volume $C_V$ undergoes a quasistatic process described by $p V^{\alpha} = \text{constant}$ in a $p-V$ diagram,where $\alpha$ is a constant. The heat capacity of the gas during this process is given by

$0.02 \, mol$ of an ideal diatomic gas with initial temperature $20^{\circ} C$ is compressed from $1500 \, cm^3$ to $500 \, cm^3$. The thermodynamic process is such that $p V^2 = \beta$,where $\beta$ is a constant. Then,the value of $\beta$ is close to (the gas constant,$R = 8.31 \, J / K / mol$).

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