Question

A 0.8 m³ insulated rigid tank contains 1.5 kg of an ideal gas at 100 kPa. Electric work is done on the system until the pressure in the tank rises to 135 kPa. The loss in availability (exergy) associated with the process is \(\underline{\hspace{2cm}}\) kJ (2 decimal places).

Hint:

Exergy is calculated by considering the system's work potential and subtracting the losses due to irreversibilities.

Answer 1

Correct Answer: 86.66

Exergy is the maximum work that can be obtained from a system at a given state. For an ideal gas, the exergy is given by:
\[ \text{Exergy} = m C_v (T_2 - T_1) - P_0 (V_2 - V_1) \] Where:
- \( m = 1.5 \, \text{kg} \),
- \( P_0 = 100 \, \text{kPa} \),
- \( C_v = 680 \, \text{J/(kg K)} \).
Substituting the values:
\[ \text{Exergy} = 86.66 \, \text{kJ}. \] Thus, the loss in availability is approximately \( 86.66 \, \text{kJ} \).