Question

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$ - diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-I with the corresponding statements in List-II.

List-I		List-II
P.	In process I	1.	Work done by the gas is zero
Q.	In process II	2	Temperature of the gas remains unchanged
R.	In process III	3	No heat is exchanged between the gas and its surroundings
S.	In process IV	4	Work done by the gas is $6 P_0 V_0$

• A. P $\to$ 4; Q $\to$ 3; R $\to$ 1; S $\to$ 2
• B. P $\to$ 1; Q $\to$ 3; R $\to$ 2; S $\to$ 4
• C. P $\to$ 3; Q $\to$ 4; R $\to$ 1; S $\to$ 2
• D. P $\to$ 3; Q $\to$ 4; R $\to$ 2; S $\to$ 1

Answer 1

Answer: (C)

Process - I is an adiabatic process
$\Delta Q = \Delta U + W \, \, \, \, \Delta Q = 0$
$W = - \Delta U$
Volume of gas is decreasing $\Rightarrow $ W < 0
$\Delta U > 0$
$\Rightarrow $ Temperatuer of gas increases.
$\Rightarrow $ No heat is exchanged between the gas and surrounding.
Process - II is an isobaric process
(Pressure remain constant)
$ W = P \Delta V = 3P_0 [3V_0 - V_0] = 6P_0V_0$
Process - III is an isochoric process
(Volume remain constant)
$\Delta Q = \Delta U + W$
$W = 0$
$\Delta Q = \Delta U$
Process - IV is an isothermal process
(Temperature remains constant)
$\Delta Q = \Delta U + W$
$\Delta U = 0$