Heat Capacity
Work In

Work done
on a system
v1
K1  (1 / 2)mv12
v2
K 2  (1 / 2)mv22
The work - energy principle
applies to all objects.
• If an object speeds up it
gains kinetic energy.
• If an object slows down it
loses kinetic energy.
W  K
Heat In
Heat into a
system

Temperature change is due
to heat (Q).
• If an object’s temperature
increases it gains heat.
T1 ,U1
T2 ,U 2
• If an object’s temperature
decreases it loses heat.
Q  T
Heat Capacity

The ratio of the change in heat to the change in
temperature is the heat capacity (C).
• Depends on material
• Depends on the mass
• Measured in J/K
Q  CT
Specific Heat

The ratio of the change in
heat to the change in
temperature is the heat
capacity (C).
• Depends on material
• independent of the mass
• Measured in J/kg-K
Q  mcT
Material
Mercury
Copper
Steel
Granite
Aluminum
Wood
Ice
Water
Specific heat
140 J/kg-K
390 J/kg-K
500 J/kg-K
840 J/kg-K
900 J/kg-K
1400 J/kg-K
2100 J/kg-K
4200 J/kg-K
Take a Shower


You are last to use the
shower today and the
temperature in the water
heater has dropped to 18 C
from the normal temperature
of 50 C. The heater holds
150 kg and has a 50 kW
heating coil.
How long should you wait
before starting your shower?

Find the heat required.
 Q = mcT = (150 kg)
(4200 J/kg-K) ( 32 C)
 Q = 2.1 x 107 J

Find the time from the
power, and set the heat to
the work.




P = W/t
t = Q / P
(2.1 x 107 J) / (5 x 104 W)
t = 4000 s = 1.1 hr
Equilibrium Temperature

Two systems in thermal contact will adjust to reach
the same temperature - thermal equilibrium

If they are thermally insulated, all the heat goes from
the hot system to the cold system.
1
2
m1c1T1  m2c2T2  0
Doing Dishes


A 1.5 kg aluminum pan is
heated to 180 C then
placed into a sink with 8 kg
water at 20 C.
 Setup the equation for an
unknown equilibrium
temperature T.
If no water boils, what is the
equilibrium temperature?
 Solve for T.
m p c p (T  Tp )  mwcw (Tw  T )  0
T
m p c pT p  mwcwTw
m p c p  mw c w
 T = 26 C
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