(A) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by the equation $T V^{\gamma-1} = \text{constant}$.There

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$T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$

(A) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by the equation $T V^{\gamma-1} = \text{constant}$.Therefore,for two different states $(P_1, V_1, T_1)$ and $(P_2, V_2, T_2)$,the relation holds as $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Thus,the correct option is $A$.

Class 11 Physics Thermodynamics Adiabatic Process

Easy

In an adiabatic process,the state of a gas is changed from $P_1, V_1, T_1$ to $P_2, V_2, T_2$. Out of the following relations,the correct one is

MHT CET 2022 All MHT CET

A
$T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$
B
$P_1 T_1^{\gamma-1} = P_2 T_2^{\gamma-1}$
C
$T_1 V_1^{\gamma} = T_2 V_2^{\gamma}$
D
$P_1 V_1^{\gamma-1} = P_2 V_2^{\gamma-1}$

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In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

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$A$ certain volume of a gas at $300 \ K$ expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $\gamma = 1.5$) (in $K$)

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The variation of pressure $P$ with volume $V$ for an ideal monatomic gas during an adiabatic process is shown in the figure. At point $A$,the magnitude of the rate of change of pressure with respect to volume is

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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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In an adiabatic process,the state of a gas is changed from $P_1, V_1, T_1$ to $P_2, V_2, T_2$. Out of the following relations,the correct one is

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Consider a cycle tyre being filled with air by a pump. Let $V$ be the volume of the tyre (fixed) and at each stroke of the pump $\Delta V$ ( < < V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from $P_1$ to $P_2$?

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

$A$ certain volume of a gas at $300 \ K$ expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $\gamma = 1.5$) (in $K$)

The variation of pressure $P$ with volume $V$ for an ideal monatomic gas during an adiabatic process is shown in the figure. At point $A$,the magnitude of the rate of change of pressure with respect to volume is

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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