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 find the work done during the expansion of air at constant pressure, we can use the formula for work done in a constant-pressure process:

\[
W = P \cdot \Delta V
\]

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

Since we have the initial and final volumes, we can find the initial volume \( V_1 \) using the ideal gas law. Then we can determine \( \Delta V = V_2 - V_1 \).

1. **Convert given values into standard units:**
   - Initial temperature, \( T_1 = 50^\circ \text{C} = 273 + 50 = 323 \, \text{K} \)
   - Pressure, \( P = 8 \, \text{bar} = 8 \times 10^5 \, \text{Pa} \)
   - Mass of air, \( m = 4 \, \text{kg} \)
   - Ideal gas constant for air, \( R = 287 \, \text{J/(kg \cdot K)} \)

2. **Find the initial volume \( V_1 \):**
   Using the ideal gas law:

   \[
   V_1 = \frac{m \cdot R \cdot T_1}{P}
   \]

   Substituting values:

   \[
   V_1 = \frac{4 \times 287 \times 323}{8 \times 10^5} = \frac{370876}{800000} \approx 0.4636 \, \text{m}^3
   \]

3. **Calculate the change in volume, \( \Delta V \):**

   \[
   \Delta V = V_2 - V_1 = 2 - 0.4636 = 1.5364 \, \text{m}^3
   \]

4. **Calculate the work done, \( W \):**

   \[
   W = P \cdot \Delta V = 8 \times 10^5 \times 1.5364 = 1229.12 \, \text{kJ}
   \]

   Rounded to match the closest answer, the work done is approximately:

   **Answer: (a) 1229.2 kJ**

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Would you like further details or have any questions?

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Here are some related questions for practice:

1. What is the change in internal energy in this constant-pressure process?
2. How much heat is absorbed in this process, assuming air behaves as an ideal gas?
3. If the pressure were variable, how would you approach calculating work?
4. What is the significance of specific heat values \( C_p \) and \( C_v \) in thermodynamic processes?
5. How does the ideal gas assumption simplify calculations in this context?

**Tip:** Always double-check unit conversions in thermodynamics problems to avoid calculation errors.

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) (Assume air as an ideal gas with R = 287 J/(kg.K), Cp = 1005 J/(kg.K), Cv = 718 J/(kg.K). Select the closest value) 
Options: 
 a. 1229.2 kJ 
 b. 1600.0 kJ 
 c. Zero 
 d. 1542.6 kJ

Learn how to calculate the work done when 4 kg of air expands at a constant pressure of 8 bar from an initial temperature of 50°C to a final volume of 2 m³. Using the ideal gas law and the constant-pressure work formula, this thermodynamics problem provides a practical application of key concepts. Ideal for students in Grades 11-12.

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