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?

(I) (i i) (Q)

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(I) (i v) (Q)

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(I V) (i i) (R)

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(I I I) (i v) (R)

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Solution

The correct option is D $(I) (i v) (Q)$
I: Work done by adiabatic process:

$W_{1 - 2} = \frac{(P_{2} V_{2} - P_{1} V_{1}}{γ - 1})$

II: Work done by isobaric process:
$W_{1 - 2} = - P V_{2} + P V_{1} = P Δ V$

III : Work done by isochoric Process :

$W_{1 - 2} = 0$ . As the volume is constant throughout the process.

IV: Work done by isothermal :
$W_{1 - 2} = - n R T l n \frac{V_{2}}{V_{1}}$

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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

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

Q. Which one of the following equations does not correctly represent the first law of thermodynamics for the given process in ideal gas?

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 ?

Q. During the thermodynamic process for an ideal gas as shown in the figure, which of the options hold true?

Q. Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non -expansion work is zero)

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