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…

Question

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 process. 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 → 2 = 1 γ - 1 P 2 V 2 - P 1 V 1 (i) Isothermal (P) (II) W 1 → 2 = - P V 2 + P V 1 (ii) Isochoric (Q) (III) W 1 → 2 = 0 (iii) Isobaric (R) (IV) W 1 → 2 = - n R T ln ⁡ V 2 V 1 (iv) Adiabatic (S) 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 ideal gas?

Aicharya · Accepted Answer

Laplace's correction of the speed of sound in ideal gas is related to adiabatic process. ;

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding…

Solution

Column – 1	Column – 2	Column – 3
(I) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal	(P)
(II) $W_{1 \to 2} = - P V_{2} + P V_{1}$	(ii) Isochoric	(Q)
(III) $W_{1 \to 2} = 0$	(iii) Isobaric	(R)
(IV) $W_{1 \to 2} = - n R T \ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic	(S)