An ideal gas in undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P – V diagram 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 1Column 2Column 3(I) (i) Isothermal(II) (ii) Isochoric(III) W1→2 = 0(iii) Isobaric(IV) (iv) Adiabatic

An ideal gas in undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P – V diagram 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) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal
(II) $W_{1 \to 2} = - {PV}_{2} + {PV}_{1}$	(ii) Isochoric
(III) W_1→2 = 0	(iii) Isobaric
(IV) $W_{1 \to 2} = - nRTln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

Linked Question 1

Which of the following options is the only correct representation of a process in which $Δ$ U = $Δ$ Q – P $Δ$ V?

(II) (iii) (S)

(II) (iv) (R)

(III) (iii) (P)

(II) (iii) (P)

Only B option is following the correct sequence of operations.

Linked Question 2

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 ?

(III) (iv) (R)

(I) (iv) (Q)

(I) (ii) (Q)

(IV) (ii) (R)

For determination of speed of sound in an ideal gas we use adianatic process. So any option - C is matching.

Linked Question 3

Which one of the following options is the correct combination ?

(IV) (ii) (S)

(III) (ii) (S)

(II) (iv) (P)

(II) (iv) (R)

Isobaric → work done =ρσv

F.L.T. = Q = U + ω

⇒ W = adiabatic = $\frac{1}{r - 1}$ (P₂v₂ – P₁v₁)

⇒ W_isochoric = ρdv = 0

⇒ W_isothermal ⇒ –nRT long $(\frac{v_{2}}{v_{1}})$