Mechanical%20equivalent

1
Mechanical equivalent of heat
Joule (1843)

• Under adiabatic conditions 1 F increase when
  772 lb dropped 1 foot
• 4.184 J 1 cal
• 1 J amount of work
• required to produce same ?Usys as 1 J of heat

2
(No Transcript)
3
Work done in expansion
Force on top of piston
It follows
Since
Total Work done
4

• Fig 3.4 Work done by a gas
• when it expands against a
• constant external pressure
• Irreversible expansion

5

• Fig 3.4 Work done by a gas
• when it expands isothermally
• against a non-constant external pressure.
• Set Pex P at each step of expansion
• System always at equilibrium
• Reversible expansion

6
Consider change of state Ti, Vi ? Tf, Vf
Internal energy is a state function ? change
can be considered in two steps
7
Change in internal energy as a function of
temperature
Slope (?U/?T)V
The heat capacity at constant volume CV
(?U/?T)V
8

• Change in internal energy
• as a function of temperature and volume
• U(T,V), so we hold one variable (V) constant,
• and take the partial derivative with respect
• to the other (T).

Slope (?U/?T)V
9
dU dq dw
Now 1st Law becomes
dU CvdT PdV
Can also define constant pressure heat capacity
CP (?q/?T)P
Finally
CP CV R
10

• At constant volume dU dq
• If system can change volume,
• dU ? dq
• Some heat into the system
• is converted to work
• ? dU lt dq
• Constant pressure processes
• much more common than constant volume processes

11
Plot of enthalpy as a function of temperature
Slope (?H/?T)P
The heat capacity at constant pressure CP
(?H/?T)P