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 I to state $2 .$ W denotes the corresponding work done on the system. The equation 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 is $n$ .

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

(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$

(ii) Isochoric

(III) $W_{1 \to 2} = 0$

(iii) Isobaric

(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$

(iv) Adiabatic

Which of the following options correctly represents the thermodynamics process that is used as a correction in the determination of the speed of sound ?

(I) (ii) (Q)

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(IV) (ii) (R)

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(III) (iv) (R)

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(I) (iv) (Q)

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Solution

The correct option is D (I) (iv) (Q)
By, Laplace speed of sound in adiabatic process = $332 m / s$
it concluded that sound waves do not exchange the energy to the medium.
& the velocity is given by= $\sqrt{\frac{γ R T}{m}}$

So, the process which involves here is adiabatic process.

Hence, option D is correct.

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Similar questions

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 I to state $2 .$ $W$ denotes the corresponding work done on the system. The equation 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 is $n$ .

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
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

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)

Which of the following options is the only correct representation of a process in which

Δ U = Δ Q - P Δ V ?

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 I to state $2 .$ W denotes the corresponding work done on the system. The equation 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 is $n$ .

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
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

Which of the following options correctly represents the thermodynamics process that is used as a correction in the determination of the speed of sound ?

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
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

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)

Which of the following options is the only correct representation of a process in which

Δ U = Δ Q - P Δ V ?

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The correct option is D (I) (iv) (Q)By, Laplace speed of sound in adiabatic process = 332 m/s it concluded that sound waves do not exchange the energy to the medium. & the velocity is given by= √γRTm So, the process which involves here is adiabatic process. Hence, option D is correct.