Is complete conversion of heat to work possible?
No!
This is a law of nature. You cannot convert heat into work without dumping some heat, according to Second Law of Thermodynamics.
Paradox involving Conversion of Heat to Work
Let’s consider an Isothermal Process.
In an Isothermal Process, thermal equilibrium is maintained. Therefore, the temperature of the system remains constant, which in turn means that Internal Energy change of the system is Zero.
ΔU = 0
Now, First Law of Thermodynamics says that the heat taken up by a System is used to perform Work and increase its temperature.
q = ΔU – w
So, in an Isothermal Process,
q = – w
Therefore, heat taken up by the system is being converted completely to work!
How is that possible!
Nature forbids us to convert Heat completely into work, but we can conclude from First Law of Thermodynamics that it is possible in an Isothermal Process!
The Explanation
To understand this discrepancy we have to delve into the intricacies of an Isothermal Process.
In an Isothermal Process, thermal equilibrium is established by keeping the system in contact with a thermostat. The function of the thermostat is to take heat away from the system, or transfer heat into the system for keeping its temperature constant.
So, in an Isothermal Process the part of the heat which is supposed to increase the temperature of the system, is pulled away by the thermostat.
Therefore, Second Law of Thermodynamics is not violated; some part of the heat taken up by the system is indeed being disposed of in the surrounding with the help of the thermostat!
The Complete Picture
Lets construct the parts of an Isothermal Process.
System takes up heat from a body maintained at higher temperature. We can call it a Hot Reservoir.
In order to withdraw heat from the system, the thermostat has to keep a body maintained at lower temperature. We can call that body a Cold Sink.
Suppose, q1 amount of heat is transferred from the Hot Reservoir to the System, and q2 amount of heat is dumped by the system to the Cold Sink, and the rest is used to do work on the surroundings.
If w is the work done by the system, then
q1 – q2 = – w
Since its Internal Energy is constant, the system is blind in regards to the heat being transferred to the cold sink. From its viewpoint, the system is taking up only (q1 – q2) amount of heat from the Hot Reservoir and converts it ‘completely’ into work.
But, the complete picture comprising both the system and the surroundings makes us understand that ‘Complete Conversion of Heat to Work’ is an illusion.
Note: It can easily be understood that the construct of an Isothermal Process is similar to the construct of a Heat Engine.
