How much work to be done in decreasing the volume of and ideal gas by an amount of `2.4xx10^(-4)m^(3)` and constant normal pressure of `1xx10^(5) N//m^(2)`

Options

A. 28 joule
B. 27 joule
C. 24 joule
D. 25 joule

Answer

To solve the problem of how much work is done in decreasing the volume of an ideal gas, we can use the formula for work done in a thermodynamic process at constant pressure. The formula is:

\[ W = P \Delta V \]

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

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Pressure, \( P = 1 \times 10^5 \, \text{N/m}^2 \)
- Change in volume, \( \Delta V = 2.4 \times 10^{-4} \, \text{m}^3 \)

**Step 2: Substitute the values into the work formula.**
Using the formula \( W = P \Delta V \):

\[ W = (1 \times 10^5 \, \text{N/m}^2) \times (2.4 \times 10^{-4} \, \text{m}^3) \]

**Step 3: Perform the multiplication.**
Calculating the work done:

\[ W = 1 \times 10^5 \times 2.4 \times 10^{-4} \]

To simplify this, we can multiply the coefficients and add the exponents:

\[ W = 2.4 \times 10^{5 - 4} = 2.4 \times 10^1 \]

**Step 4: Calculate the final value.**
Now, calculate \( 2.4 \times 10^1 \):

\[ W = 2.4 \times 10^1 = 24 \, \text{Joules} \]

### Final Answer:
The work done in decreasing the volume of the ideal gas is **24 Joules**.

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