(D) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by $p V^{\gamma} = \text{constant}$.Since density $\rho$ is def

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$p \rho^{-\gamma} = \text{constant}$

(D) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by $p V^{\gamma} = \text{constant}$.Since density $\rho$ is defined as $\rho = \frac{m}{V}$,we have $V = \frac{m}{\rho}$.Substituting this into the adiabatic equation:$p \left( \frac{m}{\rho} \right)^{\gamma} = \text{constant}$.Since mass $m$ is constant,$m^{\gamma}$ is also a constant.Therefore,$p \cdot \frac{1}{\rho^{\gamma}} = \text{constant}$.This can be written as $p \rho^{-\gamma} = \text{constant}$.

Class 11 Physics Thermodynamics Adiabatic Process

Medium

In case of an adiabatic process,the correct relation in terms of pressure $p$ and density $\rho$ of a gas is:

A
$p \rho^{\gamma} = \text{constant}$
B
$p^{\gamma} \rho^{\gamma-1} = \text{constant}$
C
$p \rho^{1-\gamma} = \text{constant}$
D
$p \rho^{-\gamma} = \text{constant}$

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Thermodynamics

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Adiabatic Process

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In case of an adiabatic process,the correct relation in terms of pressure $p$ and density $\rho$ of a gas is:

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One mole of an ideal gas $(C_p/C_v = \gamma)$ at absolute temperature $T_1$ is adiabatically compressed from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by

$A$ monatomic gas at a pressure of $100 \text{ kPa}$ expands adiabatically such that its final volume becomes $8$ times its initial volume. If the work done during the process is $180 \text{ J}$, then the initial volume of the gas is (in $\text{ cm}^3$)

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