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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