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JEE Advanced 2017 Paper 1

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An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here γ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas in n.

Column 1	Column 2	Column 3
(I) $W_{1\rightarrow2}\frac{1}{\gamma-1}(P_2V_2-P_1V_1)$	(i) Isothermal	(P)
(II) $W_{1\rightarrow2}=-P_2V_2+PV_1$	(ii) Isochoric	(Q)
(III) $W_{1\rightarrow2}=0$	(iii) Isobaric	(R)
(IV) $W_{1\rightarrow2}=-nRT\ln\left(\frac{V_2}{V_1}\right)$	(iv) Adiabatic	(S)

Section: Physics

Question : 17 of 54

Marks: +1, -0

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

[JEE Adv 2017 P1]

(I) (iv) (Q)
(III) (iv) (R)
(I) (ii) (Q)
(IV) (ii) (R)

Validate

Solution:

Laplace correction is done is correction in the determination of the speed of sound in an ideal gas, which states that the process assumed was not Isothermal but it is Adiabatic.

W_{adiabatic1\rightarrow2}=\frac{1}{\gamma-1}(P_2V_2-P_1V_1)

Corresponding graph is

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