Work Done in Basic Thermodynamic Processes
Basic goal: determine dE, dQ, and dW for general thermodynamics processes.
We now study 3 fundamental processes.
Constant Volume (Isochoric)
A constant volume process is the vertical path dV
= 0 in the PV planeup if heat is added and down if heat is
removed. Because dV = 0, the work done is
dW =  P dV = 0
The First Law of Thermodynamics then states: dE= dQ + dW = dQ.
For a monatomic ideal gas: E 
= 
3
 
2


NkT 
→ dQ 
= 
dE 
= 
3
 
2


Nk dT 
Constant Pressure (Isobaric)
A constant pressure process is a horizontal path in the PV
diagramright for expansion and left for compression.
Example: a gas in a container sealed with a freelysliding massive
piston.
The work done during gas expansion is: dW =
 P dV =  Nk dT
The First Law gives: dQ = dE  dW 
= 
3
 
2


Nk dT 
+ 
Nk dT 
= 
5
 
2


Nk dT 
Constant Temperature (Isothermal)
A constant temperature process is an isothermal path in the PV
diagrama hyperbolic isotherm.
Example: a gas in a container that is immersed in a
constanttemperature bath is allowed to expand slowly, or is compressed
slowly.
At constant temperature, the pressure of an ideal gas is: P = NkT/V.
The work done on the gas is:
W 
=  
∫_{vi}^{vf}

P dV 
=  NkT 
∫_{vi}^{vf}

1
 
V


dV 
W 
=  NkT ln 
( 
V_{f}
 
V_{i}


) 
=  P_{i} V_{i} ln 
( 
V_{f}
 
V_{i}


) 
=  P_{f} V_{f} ln 
( 
V_{f}
 
V_{i}


) 
The First Law gives: dE = dQ + dW = 0
→ dQ =  dW.
In an isothermal process, there is no change in
the internal energy of an ideal gas.
Important: The work done during any thermodynamic process is
path dependent (see transparency).