The First Law of Thermodynamics

Thermodynamics

Very general: describes “working substances” in terms of pressure, volume, temperature, ...

A thermodynamic system interacts with its surroundings by exchange of heat, by doing work, or both

A (macro)state describes the system, a process makes the system go from one state to another

State variables

state variable: precisely measurable physical property which characterizes the (macro)state of a system, independent of how the system was brought to that state

Examples: p, N, V, T, U

Any property that is a combination of state variables is a state variable itself

Definitions

If the pressure is constant during a process, it is said to be isobaric

V constant: isochoric

T constant: isothermal

no heat transfer: adiabatic/isentropic

p,V and p,T diagrams

It is often useful to plot p against V or p against T in a graph. Which processes are isothermal, isobaric, isochoric?

1

2

p

6

p

V T

3

54

Changing internal energy

How can this be achieved? by making the system do work W by heating the system Q

Note signs: W>0: work done by system Q>0: heat flows into system

reservoir

W

Q

Work

Mechanics: if gas expands in the direction of force F over distance dx the work done is Fdx.

Write as function of pressure:

F=pA, dV=Adx so W = pdV

Integral form: W = pdV

A

dx

dV

F

Work for different processes

Isochoric: V2 = V1 so W = 0

Isobaric: p is constant so

Isothermal: p varies so we must write

)(dd 12

2

1

2

1

VVpVpVpWV

V

V

V

1

2lnd1

dd2

1

2

1

2

1VV

nRTVV

nRTVV

nRTVpW

V

V

V

V

V

V

Process variables

Heat and work are variables associated with a process. They are not state variables!

1

2W

p

V

1

2W

p

V

curveunder areadVpW

The first law of thermodynamics

Q = U + W

Warning! U: ideal gas: kinetic energy only real gas: small contribution from potential energy

Warning! W: work done by gas expanding against pressure mechanical work e.g. to lift piston

Internal energy is a state variable

Experiments have shown:

Although neither Q nor W are state variables,

the internal energy is a state variable

In this sense the First Law of Thermodynamics contains more than just conservation of energy

Question

An ideal gas expands by 20% of its original volume. The work done does not depend on

a) the mass of the piston

b) what gas is in this piston

c) the pressure inside the piston

d) the pressure outside the piston

Question

When ice melts at atmospheric pressure, its volume decreases. The change in internal energy is

a) greater than the heat added

b) equal to the heat added

c) less than the heat added

d) we can’t tell

Question

When water boils at atmospheric pressure, its temperature remains 100 °C. This implies that

a) The kinetic energy of the molecules doesn’t change

b) Most of the heat added is used to expand

c) The internal energy doesn’t change

d) No heat needs to be added to the system

PS225 – Thermal Physics topicsThe atomic hypothesisHeat and heat transferKinetic theoryThe Boltzmann factorThe First Law of ThermodynamicsSpecific HeatEntropyHeat enginesPhase transitions