MECE251 Thermodynamics Lesson 4 3 The Carnot Engine

• Slides: 9

MECE-251 Thermodynamics, Lesson 4 -3: The Carnot Engine and the Second Law of Thermodynamics The first law of thermodynamics tells us how the energy stored within a control volume (kinetic, potential, internal, etc) changes with time as a result of the net energy entering the CV, the heat entering the CV, and the work done by the CV. The first law of thermodynamics DOES NOT TELL US whether any particular process will take place spontaneously. We know from experience that heat will naturally (spontaneously) flow from a high temperature area to a low temperature area. The second law of thermodynamics will help us understand what processes will occur spontaneously.

Types of Thermodynamic Cycles • The purpose of a heat engine is to do work upon the surroundings. • We put source energy in from a hot reservoir. • We extract useful work. • We reject waste energy to a cold reservoir. • The purpose of a heat pump is to supply energy to a warm body from a cool reservoir. • The purpose of a refrigerator is to extract energy from a cool body to a warm reservoir. • Both cycles require work input.

Performance of Thermodynamic Cycles The performance metric is the ratio of the desired effect over the cost need to achieve that desired effect. Efficiency of Heat Engines: Coefficient of Performance for Heat Pumps: Coefficient of Performance for Refrigerators:

The Second Law of Thermodynamics The second law of thermodynamics tells us whether or not any particular process (which has already been shown to obey the first law) will proceed spontaneously. Clausius Statement of 2 nd Law: It is impossible to construct a device which operates on a cycle whose sole effect is the transfer of heat from a cooler body to a hotter body. Kelvin-Planck Statement of 2 nd Law: It is impossible to construct a device which operates on a cycle and produces no other effect than the production of work and the transfer of heat from a single body. A new property, called entropy, s or S, will allow us to quantitatively decide whether or not a process will proceed spontaneously.

Reversibility In our classical physics course, we learned about conservative and non -conservative forces. The work done by a conservative force is independent of path. The work done by a non-conservative force is dependent upon path. Non-conservative forces and Irreversibilities Examples: friction between surfaces, I 2 R heating in a cable. All real engineering devices contain some non-conservative forces. Conservative forces and Reversible Cycles These are idealized limiting cases in which all sources of friction are neglected. In this case, we should be able to operate the cycle in the forward or reverse direction without penalty. These are not real engineering devices. The Carnot Cycle is the most famous idealized heat engine. It provides a theoretical upper limit on any real heat engine’s performance.

The Carnot Cycle W W State 3 State 42 2 -3 Insulated Hot 1 -2 Cold 3 -44 -1 State 1

Entropy • Entropy is a tabulated quantity for many engineering materials. It is given the symbol s (per unit mass) or S (for a given mass). • Entropy is a measure of the “disorder” associated with the state of matter. • The Entropy of the universe is always increasing. • We are almost always concerned about the “change in entropy” between two states. • For an ideal gas, we can approximate the change in entropy between states 1 and 2 as:

The Second Law of Thermodynamics Change of Entropy Contained Within the CV + Entropy Exiting the CV - Entropy Entering the CV + Change of Entropy of The Surroundings ≥ 0 Change in entropy during an interval of time Δt for a Control Volume: Rate of Change in entropy for a Control Volume: