U changes only by doing work or transferring heat to/from system– If work is done on the system (heat in), ΔU > 0– If system does work (heat out), ΔU < 0

– This implies that for an isolated system (the universe), U is constant.

First Law of Thermodynamics

First Law of Thermodynamics

Mathematical statement of first law:

U = q + w q = heat transferred to system w = work done on system

The first law is simply a statement of the conservation of total energy for a system

with defined energy inputs and outputs

ConcepTest #2

A system receives 575 J of heat from and delivers 325 J of work to its surroundings. What is the change in internal energy of the system?

A. +900 J B. +250 J C. -250 JD. -900 J

Distinguish betweenSystem & Surroundings

Internal Energy,Heat, and Work

dU = dq + dw

If an infinitesimal amount of heat (dq) is absorbed by the system

and an infinitesimal amount of work (dw) is done on the system,

then the change in U must be an infinitesimal amount (dU):

Look at the work term, focusing on expansion/compression work.

PV WorkThe gas in the cylinder is the system

How much work is performed on the gas in a cylinder (system) when compressing the gas?

Generically: w=-F dist

Expansion: dw=-PexdV

2

1

V

exVw P V dV

Expansion when P=0, w=-PexdV

Expand GasV = Vfinal - Vinitial is positive

Work is negative, work is done by systemSystem loses energy

2

1

(at constant pressure)work P dV P V

ex exVV V

Compress GasV = Vfinal - Vinitial is negative

Work is positive, work is done on systemSystem gains energy

Expansion when P=0, Psys= Pex

Typically, constant pressure can be used when the force is moving against the

atmosphere (when the difference in height is negligible)

2

1

(at constant pressure)work P dV P V

VV V ex ex

Pex = Psealevel

2A(g) + B(g)

Pex = Psealevel – P3cm

D(g)

Reversible ProcessesA process effected by infinitesimal changes in a variable.Proceeds through a sequence of equilibrium states.

One always remains on the surface of an equation of state An Idealized process – it takes infinitely long to carry out.

But, that’s thermodynamics, folks!

The work done by the system in a reversible expansion from A to B is the maximum work that the system can perform in changing from A to B

The system remains in equilibrium throughout the process and can be reversed by an infinitesimal change in the variable.

Reversible and Irreversible Work

Reversible: system and surroundings in equilibrium

Irreversible: system and surroundings not in equilibrium 2 1 2 2 1 2 2 10w P P P V V P V V

int exP P P exP P

1

2

The path is aportion of theeq. of statesurface

The path is notCompletely on the eq. of statesurface

Heat Transactions

When constant volume and no additional work, such as electrical work,

dU=dqV or U=qV

dU = dq + dwexp + dwe

0 0

Math for Heat CapacityU is a state function

It depends only on state, not on path to get thereU = Ufinal - Uinitial

This means mathematically* that dU is an

exact differential: f

iU dU

For now, consider a system of constant composition.U can then be regarded as a function of V, T and P.Because there is an equation of state relating V, T, and P, any two are sufficient to characterize U.So we could have U(P,V), U(P,T) or U(V,T).

*Physically, U depends on only the current system coordinates,and not on earlier ones.

Math for Heat Capacity

Exact differential review: F(x,y)So we could choose U(p,V), U(p,T) or U(V,T).

y x

F FdF dy dxx y

Let us choose U = U(V,T)When V V + dV at cons’t T,

U changes to 'T

UU U dVV

Eq of state

Or in general, 'T V

U UU U dV dTV T

For infinitesimal changes,

T V

U UdU dV dTV T

VV

U CT

T

T

UV

Some terms are familiar:

Math for Heat Capacity

Heat capacity at constant volume

Internal pressure at constant temp