(C) For an adiabatic process,the relationship between pressure $P$ and volume $V$ is given by $P V^\gamma = \text{constant}$.Using the ideal gas equat

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$T V^{\gamma - 1} = \text{constant}$

(C) For an adiabatic process,the relationship between pressure $P$ and volume $V$ is given by $P V^\gamma = \text{constant}$.Using the ideal gas equation $PV = RT$,we can express pressure as $P = \frac{RT}{V}$.Substituting this into the adiabatic equation: $\left( \frac{RT}{V} \right) V^\gamma = \text{constant}$.Since $R$ is a gas constant,we get $T V^{\gamma - 1} = \text{constant}$.

Class 11 Physics Thermodynamics Adiabatic Process

Easy

For adiabatic processes $\left( \gamma = \frac{C_p}{C_v} \right)$,which of the following relations is correct?

A
$P^\gamma V = \text{constant}$
B
$T^\gamma V = \text{constant}$
C
$T V^{\gamma - 1} = \text{constant}$
D
$T V^\gamma = \text{constant}$

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Adiabatic Process

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For adiabatic processes $\left( \gamma = \frac{C_p}{C_v} \right)$,which of the following relations is correct?

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$A$ given ideal gas with $\gamma = \frac{C_p}{C_v} = 1.5$ is at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume,the final temperature will be ..... $T$.

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{d'}{d} = 32$,then $\frac{P'}{P}$ is equal to:

If a gas of volume $400 \ cc$ at an initial pressure $P$ is suddenly compressed to $100 \ cc$,then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is $1.5$).

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$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)

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