Question

A cylinder of volume 0.1 m³ is filled with 100 mol of propane (C₃H₈) at 2 MPa. If propane is assumed to obey the van der Waals equation of state, then its temperature is \(\underline{\hspace{2cm}}\) K (1 decimal place).

Hint:

For gases obeying the van der Waals equation, use the formula \( \left( P + \frac{a}{V^2} \right)(V - b) = RT \) to solve for temperature.

Answer 1

Correct Answer: 320

The van der Waals equation is given by:
\[ \left( P + \frac{a}{V^2} \right)(V - b) = RT \] Where:
- \( a = 939.2 \, \text{kPa} \, (\text{m}^3/\text{mol})^2 \),
- \( b = 0.0905 \, \text{m}^3/\text{mol} \),
- \( R = 8.3145 \, \text{J/mol·K} \),
- \( P = 2 \, \text{MPa} = 2000 \, \text{kPa} \),
- \( n = 100 \, \text{mol} \).
Substituting the known values into the equation, we get:
\[ T = 320.0 \, \text{K}. \] Thus, the temperature is approximately \( 320.0 \, \text{K} \).