# THERMODYNAMICS2

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Thermodynamics

### Thermodynamic Systems, States and Processes :

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

### Slide 3:

“Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium. 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 (N2, O2, CO, …) 3 translational modes (x, y, z) + 2 rotational modes (wx, wy)

### Internal Energy of a Gas :

Internal Energy of a Gas A pressurized gas bottle (V = 0.05 m3), contains helium gas (an ideal monatomic gas) at a pressure p = 1×107 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?

### Changing the Internal Energy :

Changing the Internal Energy 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 = NkT ) Thermal reservoir HEAT is the transfer of thermal energy into the system from the surroundings There are two ways to change the internal energy of a system: Work and Heat are process energies, not state functions. Wby = -Won Q

### Work Done by An Expanding Gas :

Work Done by An Expanding Gas The expands slowly enough to maintain thermodynamic equilibrium.

### A Historical Convention :

A Historical Convention Energy leaves the system and goes to the environment. Energy enters the system from the environment.

### Total Work Done :

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

### Pressure as a Function of Volume :

Pressure as a Function of Volume Work is the area under the curve of a PV-diagram.

### Different Thermodynamic Paths :

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 :

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. We 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 dWby = F dx = pA dx = p (A dx)= p dV Consider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is: dx When a gas expands, it does work on its environment

### What is Heat? :

What is Heat? Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system Sign of Q : Q > 0 system gains thermal energy Q < 0 system loses thermal energy

### An Extraordinary Fact :

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.

### The First Law of Thermodynamics (FLT) :

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

### 1st Law of Thermodynamics :

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 :

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.

### Isoprocesses :

Isoprocesses apply 1st law of thermodynamics to closed system of an ideal gas isoprocess is one in which one of the thermodynamic (state) variables are kept constant use pV diagram to visualise process

### Isobaric Process :

Isobaric Process process in which pressure is kept constant

### Isochoric Process :

Isochoric Process process in which volume is kept constant

### Isothermal Process :

Isothermal Process process in which temperature is held constant

### Thermodynamic processes of an ideal gas( FLT: DU = Q - Wby ) :

Isochoric (constant volume) Thermodynamic processes of an ideal gas( FLT: DU = Q - Wby )

### Slide 22:

Isothermal (constant temperature) ( FLT: DU = Q - Wby )