Question

Determine the change in the internal energy of air, in kJ/kg, as it undergoes a change of state from 100 kPa 34°C to 100 kPa and 420°C using the equation of state P(v – a) = RT where a = 0.01 m/kg, and compare the result to the value obtained by using the ideal gas equation of state. Consider constant specific heats at average temperature.

Answer 1

To determine the change in internal energy of air as it undergoes a change of state from 100 kPa and 34°C to 100 kPa and 420°C using the given equation of state P(v – a) = RT, where a = 0.01 m3/kg, we need to know the specific heat capacity of air at constant volume cv. The change in internal energy ΔU can be calculated as ΔU = cv * ΔT, where ΔT is the change in temperature.

The average temperature between the initial and final states is (34 + 420) / 2 = 227°C. At this temperature, the specific heat capacity of air at constant volume is approximately 0.718 kJ/kg.K. Therefore, the change in internal energy of air as it undergoes the given change of state is ΔU = cv * ΔT = 0.718 kJ/kg.K * (420 - 34) K ≈ 277.5 kJ/kg.

If we use the ideal gas equation of state instead, the result would be the same since for an ideal gas, internal energy depends only on temperature and is independent of pressure and volume.