4 kg air with initial temperature of 50°C expands at a constant pressure of 8 bar to reach to a final volume 2 m3. How much work is done in this process?    (4 mark)

Whenever necessary, assume air as an ideal gas and consider R = 287 J/(kg.K), Cp = 1005 J/(kg.K), Cv = 718 J/(kg.K). (Select the closest value)

Question 7Answer

a.
1229.2 kJ


b.
1600.0 kJ


c.
Zero


d.
1542.6 kJ

To determine the work done during the constant pressure expansion of the air, we can use the formula:

\[
W = P \Delta V
\]

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

### Step 1: Converting Pressure to SI Units
Given that the pressure \( P = 8 \) bar, we first convert this to Pascals (Pa):
\[
8 \, \text{bar} = 8 \times 10^5 \, \text{Pa} = 800{,}000 \, \text{Pa}
\]

### Step 2: Initial Volume Calculation
Since air is assumed to behave as an ideal gas, we can use the ideal gas law to calculate the initial volume, \( V_1 \), using:
\[
PV = nRT
\]
or equivalently,
\[
V = \frac{mRT}{P}
\]
where:


4 kg air with initial temperature of 50°C expands at a constant pressure of 8 bar to reach to a final volume 2 m3. How much work is done in this process?

Determine the work done in a constant pressure expansion of 4 kg of air at 50°C and 8 bar to a volume of 2 m³. Learn key thermodynamic principles, including the ideal gas law and work formula W = P ΔV, with detailed steps and calculations. Suitable for college-level students studying thermodynamics.

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