(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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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

$5.6\, L$ of helium gas at $STP$ is adiabatically compressed to $0.7\, L$. Taking the initial temperature to be $T_1$,the magnitude of work done in the process is

$A$ polyatomic gas $\left( \gamma = \frac{4}{3} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_0$,its new pressure will be (in $P_0$)

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$A$ gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is $1.5$, then the percentage decrease in the volume of the gas is

One mole of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ at $127^{\circ} C$ is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its initial volume. Find the magnitude of the work done on the system in $cal$.

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