A frictionless piston-cylinder based enclosure contains some amount of gas at a pressure of 400 kPa. Then heat is transferred to the gas at constant pressure in a quasi-static process. The piston moves up slowly through a height of 10 cm. If the piston has a cross-section area of 0.3 `m^2`, the work done by the gas in this process is

Options

A. 6 kJ
B. 12 kJ
C. 7.5 kJ
D. 24 kJ

Explanation

To solve the problem, we need to calculate the work done by the gas when it expands against a piston at constant pressure. The work done by the gas can be calculated using the formula:

\[ W = P \Delta V \]

Where:
- \( W \) is the work done,
- \( P \) is the pressure,
- \( \Delta V \) is the change in volume.

### Step 1: Identify the given values
- Pressure, \( P = 400 \, \text{kPa} = 400 \times 10^3 \, \text{Pa} \) (since 1 kPa = 1000 Pa)
- Cross-sectional area of the piston, \( A = 0.3 \, \text{m}^2 \)
- Height moved by the piston, \( h = 10 \, \text{cm} = 0.1 \, \text{m} \) (since 1 cm = 0.01 m)

### Step 2: Calculate the change in volume, \( \Delta V \)
The change in volume can be calculated using the formula:

\[ \Delta V = A \times h \]

Substituting the values:

\[ \Delta V = 0.3 \, \text{m}^2 \times 0.1 \, \text{m} = 0.03 \, \text{m}^3 \]

### Step 3: Calculate the work done, \( W \)
Now, we can substitute the values of pressure and change in volume into the work done formula:

\[ W = P \Delta V \]

Substituting the values:

\[ W = 400 \times 10^3 \, \text{Pa} \times 0.03 \, \text{m}^3 \]

Calculating this gives:

\[ W = 400 \times 10^3 \times 0.03 = 12,000 \, \text{J} \]

### Step 4: Convert work done to kilojoules
Since \( 1 \, \text{kJ} = 1000 \, \text{J} \):

\[ W = \frac{12,000 \, \text{J}}{1000} = 12 \, \text{kJ} \]

### Final Answer
The work done by the gas in this process is **12 kJ**.

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