Question

For the Refrigerant R-134 (at 1 MPa and 50°C), the difference between the specific volume computed by assuming it to be an ideal gas and its actual specific volume is: \( v_{\text{ideal}} - v_{\text{actual}} = 4.529 \times 10^{-3} \, \text{m}^3/\text{kg} \). If the compressibility factor associated with this state is \( Z = 0.84 \), then \( v_{\text{com}} - v_{\text{actual}} = \underline{\hspace{2cm}} \times 10^{-3} \, \text{m}^3/\text{kg} \) (3 decimal places).

Hint:

For refrigerants, use the compressibility factor to calculate the real specific volume from the ideal specific volume.

Answer 1

Correct Answer: 0.3

The compressibility factor \( Z \) is given by the relation:
\[ v_{\text{com}} = Z v_{\text{ideal}} \] We are given that:
- \( v_{\text{ideal}} - v_{\text{actual}} = 4.529 \times 10^{-3} \, \text{m}^3/\text{kg} \),
- \( Z = 0.84 \), and
- \( v_{\text{actual}} = 4.529 \times 10^{-3} \, \text{m}^3/\text{kg} \).
Thus:
\[ v_{\text{com}} - v_{\text{actual}} = 0.84 \times 4.529 \times 10^{-3} - 4.529 \times 10^{-3} = 0.300 \times 10^{-3} \, \text{m}^3/\text{kg}. \] So, \( v_{\text{com}} - v_{\text{actual}} \approx 0.300 \times 10^{-3} \, \text{m}^3/\text{kg} \).