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MAE 334
Lab 3
If the apparatus were perfectly insulated, all of the mechanical work would go into
heating the cylinder. Actually, some heat is continually lost to the surroundings. If P is
the rate of mechanical work (in Watts) and Q is the rate of heat loss to the surroundings
(also in Watts), the calorimeter gains energy at a rate:
(1)
Q
P
dt
dE
−
=
For the calorimeter, the relationship between energy gain and temperature rise is
proportional to its thermal capacity:
dt
dT
cm
dt
dE
cal
=
(2)
Here, the thermal capacity in Joules per degree Celsius (J/C) is the product of the specific
heat of aluminum (
) and the mass of the calorimeter (
). Also, the heat loss to the
surroundings is proportional to the temperature difference between the cylinder and the
laboratory surroundings:
c
cal
m
(3)
)
(
lab
T
T
H
Q
−
=
where the overall convection factor H in Watts per degree Celsius (W/C) is the product of
the convective heat transfer coefficient (h) and the surface area of the calorimeter (A).
Thus,
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 Spring '09

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