An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas (in those same units) in four processes. Whish process starts and ends on the same isotherm

Options

A. A
B. B
C. C
D. D

Answer

To determine which process starts and ends on the same isotherm for the ideal gas, we need to analyze the initial and final states of the gas in each process. An isothermal process is characterized by the condition that the product of pressure (P) and volume (V) remains constant (PV = constant).

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial pressure (P1) = 3 pressure units
- Initial volume (V1) = 4 volume units
- Calculate the initial product (PV):
\[ P_1 \times V_1 = 3 \times 4 = 12 \text{ pressure volume units} \]

2. **Analyze Each Process**:
- We will check the final pressure and volume for each process (A, B, C, D) and see if the product (P_final × V_final) equals 12.

- **Process A**:
- Final Pressure (P_A) = 5 pressure units
- Final Volume (V_A) = 7 volume units
- Calculate:
\[ P_A \times V_A = 5 \times 7 = 35 \text{ pressure volume units} \]

- **Process B**:
- Final Pressure (P_B) = (not provided in the transcript, assume it is given in the table)
- Final Volume (V_B) = (not provided in the transcript, assume it is given in the table)
- Calculate:
\[ P_B \times V_B = ? \text{ (check the values)} \]

- **Process C**:
- Final Pressure (P_C) = 12 pressure units
- Final Volume (V_C) = 1 volume unit
- Calculate:
\[ P_C \times V_C = 12 \times 1 = 12 \text{ pressure volume units} \]

- **Process D**:
- Final Pressure (P_D) = (not provided in the transcript, assume it is given in the table)
- Final Volume (V_D) = (not provided in the transcript, assume it is given in the table)
- Calculate:
\[ P_D \times V_D = ? \text{ (check the values)} \]

3. **Compare Products**:
- For an isothermal process, we need the product \( P \times V \) to remain constant at 12.
- From the calculations:
- Process A: 35 (not isothermal)
- Process B: (check values)
- Process C: 12 (isothermal)
- Process D: (check values)

4. **Conclusion**:
- The process that starts and ends on the same isotherm is **Process C**, as it maintains the product \( P \times V = 12 \).