(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^{\

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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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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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If during an adiabatic process the pressure of a mixture of gases is found to be proportional to the square of its absolute temperature,the ratio of $C_p / C_v$ for the mixture of gases is .........

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$1 \, \text{kmol}$ of an ideal gas is compressed adiabatically,requiring $146 \, \text{kJ}$ of work. During this process,the temperature of the gas increases by $7^o \text{C}$. The gas is: $(R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1})$

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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

An ideal gas expands adiabatically $(\gamma = 1.5)$. To reduce the r.m.s. velocity of the molecules $3$ times, the gas has to be expanded by a factor of: (in $\times$)

$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The adiabatic constant for the gas is $\gamma = 3/2$. The work done by the gas in the process is: $(\mu = 1 \text{ mole})$

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.

If during an adiabatic process the pressure of a mixture of gases is found to be proportional to the square of its absolute temperature,the ratio of $C_p / C_v$ for the mixture of gases is .........

$1 \, \text{kmol}$ of an ideal gas is compressed adiabatically,requiring $146 \, \text{kJ}$ of work. During this process,the temperature of the gas increases by $7^o \text{C}$. The gas is: $(R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1})$

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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.