PhysicsLAB: Specific Heat and the Law of Heat Exchange

ΣQ_lost + ΣQ_gained = 0 where
Q = mcΔT and ΔT = T_f - T_o

Notes: this formula for heat lost or heat gained only applies when there is no change in phase. In the English system, heat is measured in calories where 4.186 J = 1 calorie. A calorie is defined as the amount of heat required to raise one gram of water 1 Cº. A calorie in a dietbook is a kilocalorie, or 1000 calories, which equals 4186 J.

c_water = 4186 J/kgC°

c_glass = 840 J/kgC°

c_silver = 240 J/kgC°

c_{human body} = 3470 J/kgC°

1. Hypothermia can occur if the body temperature drops to 35.0°C, although people have been known to survive much lower temperatures. On January 19, 1985, 2-year-old Michael Trode was found in the snow near his Milwaukee home with a body temperature of 16.0°C. If Michael's mass was 10.0 kg, how much heat did his body lose, assuming his normal body temperature was 37.0°C? (Happily, Michael survived!)

2. Peter is heating water on the stove to boil eggs for a picnic. How much heat is required to raise the temperature of his 10.0 kg pot of water from 20.0°C to 100.°C?

3. Emily is testing her baby's bath water and finds that it is too cold, so she adds some hot water from a kettle on the stove. If Emily adds 2.00 kg of water at 80.0°C to 20.0 kg of bath water at 27.0°C, what is the final temperature of the bath water?

4. Nils is emptying the dishwasher. He removes a 0.200 kg glass that has a temperature of 30.0°C. Into it he pours 0.100 kg of diet soda (mostly water) which comes out of the refrigerator with a temperature of 5.00°C. Assuming no external heat loss, what will be the final equilibrium temperature of the glass of diet soda (no ice was added)?

5. Gwyn's insulated bowl is filled with 0.175 kg of 60.0°C soup (mostly water) that she stirs with a 20.0°C silver spoon of mass 0.0400 kg. the spoon slips out of her hand and slides into the soup. What equilibrium temperature will be reached if the spoon is allowed to remain in the soup and no heat is lost to the outside air? (For simplicity, assume that the temperature of the bowl does not change.)