(D) For an adiabatic process,the relationship between pressure $P$ and density $\rho$ (or $d$) is given by $P \propto \rho^\gamma$. Thus,$\frac{P^{\pr

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(D) For an adiabatic process,the relationship between pressure $P$ and density $\rho$ (or $d$) is given by $P \propto \rho^\gamma$. Thus,$\frac{P^{\prime}}{P} = \left(\frac{d^{\prime}}{d}\right)^\gamma$. Given $\frac{d^{\prime}}{d} = 32$ and $\gamma = \frac{7}{5}$. Substituting these values: $\frac{P^{\prime}}{P} = (32)^{7/5}$. Since $32 = 2^5$,we have $\frac{P^{\prime}}{P} = (2^5)^{7/5} = 2^7$. Calculating $2^7 = 128$. Therefore,the ratio $\frac{P^{\prime}}{P} = 128$.

Class 11 Physics Thermodynamics Adiabatic Process

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The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$.

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A
$\frac{1}{128}$
B
$\frac{1}{64}$
C
$64$
D
$128$

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When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process:

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Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

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During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

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$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

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An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

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The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$.

Similar Questions

When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process:

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

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Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.