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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