(B) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = \text{constant}$.Given the condition

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(B) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = \text{constant}$.Given the condition $T \propto \frac{1}{\sqrt{V}}$,we can write this as $T \propto V^{-1/2}$,which implies $TV^{1/2} = \text{constant}$.Comparing the two expressions $TV^{\gamma-1} = \text{constant}$ and $TV^{1/2} = \text{constant}$,we get $\gamma - 1 = \frac{1}{2}$.Solving for $\gamma$,we find $\gamma = 1 + 0.5 = 1.5$.

Class 11 Physics Thermodynamics Adiabatic Process

Easy

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $\gamma$ for the gas is $(\gamma = \frac{C_p}{C_v}, V = \text{Volume of the gas})$

MHT CET 2021 All MHT CET

A
$1.8$
B
$1.5$
C
$1.3$
D
$1.4$

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Thermodynamics

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Adiabatic Process

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MediumMHT CET 2024

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EasyAIPMT 1998

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The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

DifficultMHT CET 2023

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One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $\gamma$ for the gas is $(\gamma = \frac{C_p}{C_v}, V = \text{Volume of the gas})$

Similar Questions

An ideal gas is expanded adiabatically at an initial temperature of $300 \ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$.

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

The $P-V$ graph of an ideal gas cycle is shown. The adiabatic process is described by the region

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process,which of the following is true?

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

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