# the internal energy of a.. u = 3.64 pv + 90. solved problem

#### The following equation gives the internal energy of a certain substance u = 3.64 pv + 90 where u is kJ/kg, p is in kPa and v is in m3/kg. A system composed of 3.5 kg of this substance expands from an initial pressure of 500 kPa and a volume of 0.25 m3 to a final pressure 100 kPa in a proces in which pressure and volume are related by pv1.25 = constant. (i) If the expansion is quasi-static, find Q, ΔU and W for the process. (ii) In another process, the same system expands according to the same pressure-volume relationship as in part (i), and from the same initial stale to the same final state as in part (i), but the heat transfer in this case is 32 kJ. Find the work transfer for this process. (iii) Explain the difference in work transfer in parts (i) and (ii).

The following equation gives the internal energy of a certain substance

u = 3.64 pv + 90

where u is kJ/kg, p is in kPa and v is in m3/kg.

A system composed of 3.5 kg of this substance expands from an initial pressure of 500 kPa and a volume of 0.25 m3 to a final pressure 100 kPa in a proces in which pressure and volume are related by pv1.25 = constant.

(i) If the expansion is quasi-static, find Q, ΔU and W for the process.

(ii) In another process, the same system expands according to the same pressure-volume relationship as in part (i), and from the same initial stale to the same final state as in part (i), but the heat transfer in this case is 32 kJ. Find the work transfer for this process.

(iii) Explain the difference in work transfer in parts (i) and (ii).