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

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(A) For an adiabatic process, the relationship between temperature and volume is given by $T V^{\gamma - 1} = \text{constant}$.Since the gas is monoatomic, the adiabatic index $\gamma = 5/3$.Therefore, $\gamma - 1 = 5/3 - 1 = 2/3$.The volume of the gas in a cylinder of cross-sectional area $A$ is $V = A \times L$.Thus, $T_1 (A L_1)^{2/3} = T_2 (A L_2)^{2/3}$.Rearranging the terms, we get $(T_2 / T_1) = (L_1 / L_2)^{2/3}$.

Class 11 Physics Thermodynamics Adiabatic Process

Medium

$A$ monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $T_2$. If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively, then $(T_2 / T_1)$ is given by

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A
$(L_1 / L_2)^{2/3}$
B
$(L_2 / L_1)^{2/3}$
C
$(L_1 / L_2)$
D
$(L_2 / L_1)$

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Two different adiabatic paths for the same gas intersect two isothermal curves as shown in the $P-V$ diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

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The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).

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$A$ monoatomic ideal gas, initially at temperature $T_{1}$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

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We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system,which of the following statements is true?

$A$ monoatomic gas is compressed adiabatically to $1/8$ of its initial volume. What happens to the gas pressure? $(\gamma = 5/3)$

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