Converting heat to work

For an engine made to convert heat into work we have

Where is the heat we must deliver to the system to make it operate. The second law of thermodynamics sets limits for the efficiency of such a process. Specifically we can show that a cyclic process whose only effect is to convert heat into work is in conflict with the second law of thermodynamics. To prove this assume that we had such a process. We calculate the change in entropy for the closed system consisting of the working substance and the reservoir which delivers heat to the cyclic process. To calculate the total change in entropy during a cycle we add the changes in entropy associated with each component of the system: reservoir delivering heat and working substance. For a cyclic process the entropy of the working substance (gas) cannot change through one stroke of the process. However the entropy of the reservoir(s) delivering heat will change by an amount

Because heat flows from this system (dQ<0) and . According to the second law of thermodynamics this is not possible. In fact an alternative formulation due to Lord Kelvin of the second law is that

No process is possible whose only effect is the absorption of heat from a thermal reservoir and the complete conversion of this energy into work

Last time we discussed the most efficient thermodynamic process possible for converting heat to work. This is the so-called Carnot cycle for which