Question

Find the total work the heat engine can give out as it receives energy from the rock bed of 2 m³ which is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock bed therefore cools down and as it reaches 290 K the process stops. write the entropy balance equation for the control volume that is the combination of the rock bed and the heat engine

Answer 1

To get the work we must integrate over the process or do the 2^nd law for a control volume around the whole setup out to T₀ C.V. 

Heat engine plus rock bed out to T₀. W and Q_L goes out.