Question

Match List-I with List-II.

Choose the correct answer from the options given below :

• A. (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
• B. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
• C. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
• D. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Hint:

Remember the definitions of the four basic thermodynamic processes: - Isothermal: constant temperature (\( \Delta T = 0 \), implies \( \Delta U = 0 \) for ideal gas).
- Adiabatic: no heat exchange (\( \Delta Q = 0 \)).
- Isobaric: constant pressure (\( \Delta P = 0 \)).
- Isochoric: constant volume (\( \Delta V = 0 \), implies \( \Delta W = 0 \)).

Answer 1

The Correct Option is C

Step 1: Understand the characteristics of each thermodynamic process listed in List-I.
(A) Isothermal process:
An isothermal process occurs at a constant temperature (\( \Delta T = 0 \)). For an ideal gas, the internal energy \( U \) is directly proportional to temperature.
Therefore, in an isothermal process for an ideal gas, the change in internal energy is zero (\( \Delta U = 0 \)). So, (A) matches with (IV).
(B) Adiabatic process:
An adiabatic process is one in which no heat is exchanged with the surroundings (\( \Delta Q = 0 \)). So, (B) matches with (II).
(C) Isobaric process:
An isobaric process occurs at a constant pressure (\( \Delta P = 0 \)). In general, for an isobaric process, work is done by or on the system (\( \Delta W \neq 0 \)), and heat is exchanged (\( \Delta Q \neq 0 \)), leading to a change in internal energy (\( \Delta U \neq 0 \)). So, (C) matches with (III).
(D) Isochoric process:
An isochoric process (also called isovolumetric) occurs at a constant volume (\( \Delta V = 0 \)). Since work done \( \Delta W = P \Delta V \), in an isochoric process, the work done is zero (\( \Delta W = 0 \)). So, (D) matches with (I).
Step 2: Match the thermodynamic processes with their corresponding characteristics.
(A) Isothermal - \( \Delta U = 0 \) - (IV) (B) Adiabatic - \( \Delta Q = 0 \) - (II) (C) Isobaric - \( \Delta U \neq 0 \) - (III) (D) Isochoric - \( \Delta W = 0 \) - (I)
Step 3: Choose the correct option based on the matching.
The correct matching is (A)-(IV), (B)-(II), (C)-(III), (D)-(I), which corresponds to option (3).