Heat and Heat Transfer

1. Even when shut down after a period of normal use, a large commercial nuclear reactor produces heat at the rate of 157 MW by the radioactive decay of fission products. This causes a rapid increase in temperature if the cooling system fails.

(a) Calculate the rate of temperature increase in degrees Celsius per second (°C/s), if the mass of the reactor core is 1.60  105 kg and has an average specific heat of 0.0800 kcal/(kg · °C).

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(b) How long would it take to obtain a temperature increase of 1700°C? (The initial rate of temperature increase would be greater than calculated here, because the heat is concentrated in a smaller mass, but later, the temperature increase would slow because the 5 ✕ 105-kg steel containment vessel would begin to be heated, too.)


2. Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 24 rubs a distance of 7.50 cm each and with a frictional force averaging 75.3 N, what is the temperature increase? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers. The specific heat of the tissue is 3500 J/(kg · °C).


3. Samantha wishes to maintain her weight and goes to the gym to work off the calories she consumed at breakfast that morning. She lifts a 20.0-kg barbell from shoulder level to above her head, through a vertical height of 0.550 m. How many times must she lift the barbell to make up for the 3.00  102 Calories of energy she consumed at breakfast? Note that Calories refers to food calories. (Include lowering the barbell as well.)


4. The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 265 g of hot coffee initially at 86.0°C if 2.43 g evaporates from it? The coffee is in a Styrofoam cup, and so other methods of heat transfer can be neglected. Assume that coffee has the same physical properties as water; its latent heat of vaporization is 539 kcal/kg and its specific heat is 1.00 kcal/(kg · °C).


5. On a hot dry day, evaporation from a lake takes away just enough heat to balance the 0.907 kW/m2 of incoming sunlight. What mass of water evaporates in 2.20 h from each square meter? Use the latent heat of vaporization for water at 37°C to be 580 kcal/kg.


6. Radiant heat makes it impossible to stand close to a hot lava flow. Calculate the rate of heat loss by radiation from 1.00 m2 of 1290°C fresh lava into 38.2°C surroundings, assuming lava’s emissivity is 1.


7. Find the net rate of heat loss by radiation from a skier standing in the shade, given the following. She is completely clothed in white (head to foot, including a ski mask), the clothes have an emissivity of 0.200 and a surface temperature of 14.0°C, the surroundings are at −15.3°C,and her surface area is 1.42 m2.


8. Suppose you walk into a sauna that has an ambient temperature of 51.5°C.

(a) Calculate the rate of heat transferred to you by radiation given your skin has a temperature of 37.0°C, an emissivity of 0.98, and the surface area of your body is 1.70 m2.


(b) If all other forms of heat transfer are balanced (net zero), at what rate will your body temperature increase if your mass is 58 kg? (Assume 3500 J/(kg · °C) is the specific heat of the human body.)


9. The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly windows conduct heat, calculate the rate of conduction in watts through a 3.52 m2 window that is 0.655 cm thick if the temperatures of the inner and outer surfaces are 5.00°C and −10.0°C, respectively. This rapid rate will not be maintained — the inner surface will cool, and frost may even form. The thermal conductivity of glass is 0.84 J/(s · m · °C).


10. Suppose you stand with one foot on ceramic flooring and one on a wool carpet, making contact over a 79.2 cm2 area with each foot. Both the ceramic and the carpet are 2.00 cm thick and are 10.0°C on their bottoms. At what rate must each foot supply heat to keep the top of the ceramic and carpet at 33.0°C? The thermal conductivity of ceramic is 0.84 J/(s · m · °C) and that of wool is 0.04 J/(s · m · °C).

ceramic tile = W
wool carpet = W