(C) The given process equation is $PV^2 = C$.Using the ideal gas law $PV = nRT$,we can write $P = \frac{nRT}{V}$.Substituting this into the process eq

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If $V_2 > V_1$ then $T_2 < T_1$

(C) The given process equation is $PV^2 = C$.Using the ideal gas law $PV = nRT$,we can write $P = \frac{nRT}{V}$.Substituting this into the process equation: $(\frac{nRT}{V})V^2 = C$.This simplifies to $nRTV = C$,or $TV = \text{constant}$ (since $nR$ and $C$ are constants).Therefore,$T_1 V_1 = T_2 V_2$,which implies $\frac{T_1}{T_2} = \frac{V_2}{V_1}$.If $V_2 > V_1$,then $\frac{V_2}{V_1} > 1$,which means $\frac{T_1}{T_2} > 1$,so $T_1 > T_2$ or $T_2 Thus,option $C$ is correct.

Class 11 Physics Thermodynamics Polytropic Process

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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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If $P_1 > P_2$ then $T_1 < T_2$
B
If $V_2 > V_1$ then $T_2 > T_1$
C
If $V_2 > V_1$ then $T_2 < T_1$
D
If $P_1 > P_2$ then $V_1 > V_2$

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$1 \, \text{mole}$ of a gas expands with temperature as $V = KT^{2/3}$. What is the work done when temperature changes by $30^oC$ (in $R$)?

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The figure shows a process $AB$ undergone by $2$ moles of an ideal diatomic gas. The process $AB$ follows the relation $VT = \text{constant}$. Given $T_1 = 300 \text{ K}$ and $T_2 = 500 \text{ K}$ ($R$ is the gas constant).

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One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

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Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition $V \propto T^{2/3}$. $[R = 1.99 \ cal/mol-K]$

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An ideal gas expands in such a way that $PV^2 = \text{constant}$ throughout the process.

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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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$1 \, \text{mole}$ of a gas expands with temperature as $V = KT^{2/3}$. What is the work done when temperature changes by $30^oC$ (in $R$)?

The figure shows a process $AB$ undergone by $2$ moles of an ideal diatomic gas. The process $AB$ follows the relation $VT = \text{constant}$. Given $T_1 = 300 \text{ K}$ and $T_2 = 500 \text{ K}$ ($R$ is the gas constant).

One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition $V \propto T^{2/3}$. $[R = 1.99 \ cal/mol-K]$

An ideal gas expands in such a way that $PV^2 = \text{constant}$ throughout the process.

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