Calculate the specific volume of 2 kg of air at a pressure of 150 kPa and a temperature of 25C.Assume air behaves as an ideal gas.

To calculate the specific volume (\( v \)) of air, we can use the Ideal Gas Law:

\[
PV = nRT
\]

Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles of air,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

We can rearrange the Ideal Gas Law to solve for specific volume (\( v \)):

\[
v = \frac{RT}{P}
\]

Specific volume is defined as the volume per unit mass. For air, \( R \) (specific gas constant) is typically taken as \( R = 287 \, \text{J/kg·K} \).

### Given:
- Mass \( m = 2 \, \text{kg} \),
- Pressure \( P = 150 \, \text{kPa} = 150,000 \, \text{Pa} \),
- Temperature \( T = 25^\circ C = 25 + 273.15 = 298.15 \, \text{K} \).

Now, using the formula for specific volume:

\[
v = \frac{R T}{P}
\]

Substituting the values:

\[
v = \frac{287 \times 298.15}{150,000} \, \text{m}^3/\text{kg}
\]

Let me calculate this.The specific volume of the air is approximately \( 0.570 \, \text{m}^3/\text{kg} \).

If you have any questions or want further details, feel free to ask!

Here are 5 related questions for further exploration:
1. How would the specific volume change if the temperature increased to 50°C?
2. What happens to the specific volume if the pressure is doubled?
3. How is the specific volume affected if the mass is doubled but the conditions remain the same?
4. Can you derive the Ideal Gas Law from basic thermodynamic principles?
5. How does assuming ideal gas behavior affect the accuracy of these calculations for real gases?

**Tip:** Always ensure the temperature is converted to Kelvin when using the Ideal Gas Law.

Calculate the specific volume of 2 kg of air at a pressure of 150 kPa and a temperature of 25C. Assume air behaves as an ideal gas.

Learn how to calculate the specific volume of 2 kg of air at 150 kPa and 25°C using the Ideal Gas Law. This detailed solution covers key thermodynamic concepts, unit conversions, and the specific gas constant for air. Suitable for undergraduate students in engineering or physics.

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