Thermodynamics

Thermodynamic Systems, States and Processes Objectives are to: define thermodynamics systems and states of systems explain how processes affect such systems apply the above thermodynamic terms and ideas to the laws of thermodynamics

l “Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium. Internal Energy of a Classical ideal gas Internal Energy of a Classical ideal gas At room temperature, for most gases : monatomic gas (He, Ne, Ar, …) 3 translational modes (x, y, z) diatomic molecules (N 2, O 2, CO, …) 3 translational modes (x, y, z) + 2 rotational modes (wx, wy)

Internal Energy of a Gas A pressurized gas bottle (V = 0.05 m 3 ), contains helium gas (an ideal monatomic gas) at a pressure p = 1×10 7 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?

Changing the Internal Energy l U is a “state” function --- depends uniquely on the state of the system in terms of p, V, T etc. (e.g. For a classical ideal gas, U =  ) WORK done by the system on the environment Thermal reservoir HEAT is the transfer of thermal energy into the system from the surroundings l There are two ways to change the internal energy of a system: Work and Heat are process energies, not state functions. W by = -W on Q

Work Done by An Expanding Gas The expands slowly enough to maintain thermodynamic equilibrium. Increase in volume, dV +dV Positive Work (Work is done by the gas) -dV Negative Work (Work is done on the gas)

A Historical Convention Energy leaves the system and goes to the environment. Energy enters the system from the environment. +dV Positive Work (Work is done by the gas) -dV Negative Work (Work is done on the gas)

Total Work Done To evaluate the integral, we must know how the pressure depends (functionally) on the volume.

Pressure as a Function of Volume Work is the area under the curve of a PV-diagram. Work depends on the path taken in “PV space.” The precise path serves to describe the kind of process that took place.

Different Thermodynamic Paths The work done depends on the initial and final states and the path taken between these states.

Work done by a Gas Note that the amount of work needed to take the system from one state to another is not unique! It depends on the path taken. lWe generally assume quasi-static processes (slow enough that p and T are well defined at all times): This is just the area under the p-V curve V p p V p V dW by = F dx = pA dx = p (A dx)= p dV l Consider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is: dx l When a gas expands, it does work on its environment

An Extraordinary Fact The work done depends on the initial and final states and the path taken between these states. BUT, the quantity Q - W does not depend on the path taken; it depends only on the initial and final states. Only Q - W has this property. Q, W, Q + W, Q - 2W, etc. do not. So we give Q - W a name: the internal energy.

-- Heat and work are forms of energy transfer and energy is conserved. The First Law of Thermodynamics (FLT)  U = Q + W on work done on the system change in total internal energy heat added to system or  U = Q - W by State Function Process Functions

1st Law of Thermodynamics statement of energy conservation for a thermodynamic system internal energy U is a state variable W, Q process dependent

The First Law of Thermodynamics What this means: The internal energy of a system tends to increase if energy is added via heat (Q) and decrease via work (W) done by the system.... and increase via work (W) done on the system. Efficiency of the engine (e) ratio of the work to the heat absorbed

The Carnot Cycle

Carnot Engine Carnot cycle run in forward direction along abcda- Carnot Engine a b c d Q2 w Q1

Carnot Refrigerator Carnot cycle run in reverse direction along adcba a b c d Q2 w Q2+w

In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process. Changes are infinitesimally small in a reversible process. Efficiency of heat engine (e) in terms of absolute temperature

Carnot’s Theorem The efficiency of any heat engine operating between two heat reservoirs of high and low temperatures is never greater than the efficiency of a Carnot engine; the efficiency of any reversible engine equals the efficiency of a Carnot engine.

Irreversible processes cannot be undone by exactly reversing the change to the system. All Spontaneous processes are irreversible. All Real processes are irreversible.

Entropy Entropy (S) is a term coined by Rudolph Clausius in the 19th century. Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, QTQT

Entropy can be thought of as a measure of the randomness of a system. It is related to the various modes of motion in molecules.

Second Law of Thermodynamics The second law of thermodynamics: The entropy of the universe does not change for reversible processes and increases for spontaneous processes. Reversible (ideal): Irreversible (real, spontaneous):

Third Law of Thermodynamics The third law of thermodynamics: the entropy of a system at absolute zero is zero.