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First Law for a Thermodynamic Cycle

This phase diagram shows that the process path for a cycle begins and ends at the same state.

Since the initial and final states are identical in a thermodynamic cycle, the system experiences no net change in state. Therefore, the system also experiences no net change in energy for the cycle.

OR :

In words, the

first law of thermodynamics

or the

conservation of energy principle

applied to a

cycle

Net Energy Transferred by
Heat for the Cycle

Net Energy Transferred by Work for the Cycle

Lesson 4F: page 2 of 13

Ch4, Lesson F, Page 2 - First Law for a Thermodynamic Cycle

Consider a system that moves one time through a thermodynamic cycle.
The total energy of the system is a state variable.
Since the system begins and ends the cycle in the same state, E1 = E2 and the change in total energy for the cycle must be zero.
That simplifies the 1st Law for us.
What about the change in internal energy for the cycle ?
Internal energy is also a state variable, so ΔU must also be zero.
This leaves us with a pretty simple expression of the 1st Law for a cycle: Q = W.
I hope you can see the connection to the steam engines that motivated the development of the classical thermodynamic theory that we are studying.
The NET amount of work that you can get OUT of a thermodynamic cycle is equal to the NET amount of heat that you put IN.
This seems simple enough, right ?
Not quite. You will learn in Chapter 6 that if you put one kJ of heat into a power cycle, you get LESS than 1 kJ of work out. Where did the rest of the energy go ? It comes OUT as wasted heat. Bummer.
We will come back to that later. Now, let’s get better acquainted with cycles.

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