Question

A system of ideal gas undergoes a thermodynamic process in which the initial pressure and volume are equal to the final pressure and volume. Let △Q is the heat supplied to the system,△W is the work done by the system and △U is the change in internal energy. The correct option is: 

• A. △Q=△W
• B. △U>0
• C. △U\(\neq\)0
• D. △U+△Q+△W=0
• E. △Q+△W=0

Answer 1

The Correct Option is A

Given conditions: \[ P_i = P_f \] \[ V_i = V_f \]

First Law of Thermodynamics: \[ \Delta U = \Delta Q - \Delta W \]

For ideal gas: \[ U = U(T) \text{ (depends only on temperature)} \]

From ideal gas equation: \[ PV = nRT \] \[ \text{Since } P_iV_i = P_fV_f \Rightarrow T_i = T_f \]

Internal energy change: \[ \Delta U = 0 \text{ (since temperature is constant)} \]

First Law becomes: \[ 0 = \Delta Q - \Delta W \] \[ \Delta Q = \Delta W \]

Answer 2

1. Understand the thermodynamic process:

The problem states that the initial and final pressures and volumes are equal. This means the system undergoes a cyclic process, returning to its initial state.

2. Apply the first law of thermodynamics:

The first law of thermodynamics states:

\[\Delta U = \Delta Q - \Delta W\]

where:

• ΔU is the change in internal energy
• ΔQ is the heat supplied to the system
• ΔW is the work done by the system

3. Consider the cyclic process:

For a cyclic process, the system returns to its initial state, meaning the change in internal energy is zero:

\[\Delta U = 0\]

4. Analyze the options:

• (A) ΔQ = ΔW: Since ΔU = 0, the first law becomes \(0 = \Delta Q - \Delta W\), so ΔQ = ΔW. This is CORRECT.
• (B) ΔU > 0: ΔU = 0 for a cyclic process. This is INCORRECT.
• (C) ΔU ≠ 0: ΔU = 0 for a cyclic process. This is INCORRECT.
• (D) ΔU + ΔQ + ΔW = 0: Since ΔU = 0 and ΔQ = ΔW, this would imply 2ΔQ = 0, which is only true if no heat is exchanged. This can only occur if no work is also done. This is INCORRECT.
• (E) ΔQ + ΔW = 0: Since ΔQ = ΔW, this would imply 2ΔQ=0, which, as stated above can only occur if no heat and work are done, so this is INCORRECT

Final Answer: The correct option is \(\boxed{A}\)