#2 #6 #12 #20 #22 #242. If the temperature of 800 grams of water drops 5 degrees C, how much heat is released?
6. A physics student foolishly wants to lose weight by drinking cold water. If he drinks one liter (1000 cubic centimeters) of water 10 degrees below body temperature, how many Calories will it take to warm the water up?
We need the mass of the water for our heat energy equation. One cubic centimeter of water has a mass of one gram, so the mass of water the student drinks is one-thousand grams.
Note that it takes one-thousand little "c" calories to get a single big "C" Calorie.
12. If 200 grams of water at 100 degrees C are mixed with 300 grams of water at 50 degrees C in a completely insulated container, what is the final equilibrium temperature?
The heat lost by the hot (100 degree C) water plus the heat gained by the warm (50 degree C) water must be zero since energy is conserved. We write this as
Denoting the final equilibrium temperature as T with a subscript of f, the change in the heat energy of the warm water is given by
The heat energy change of the hot water is
Plugging the heat change of the warm and hot water into the energy conservation equation above, we have
20. How much energy would be required to raise the temperature of a 10-gram gold wedding band from room temperature (20 degrees C) to body temperature (37 degrees C)?
The specific heat of gold is found in Table 9-1 on page 206. We need this to find the heat energy to raise the temperature of the ring.
22. How much heat is required to convert 400 grams of ice at -5 degrees C to water at +5 degrees C?
The energy needed to convert the ice at -5 degrees C to water at 5 degrees C can be thought to have three parts. These are the heat needed to warm the ice to 0 degrees C, the heat to melt the ice to water at 0 degrees C, and the heat to warm the water to 5 degrees C. That is,
We must compute each of the three parts separately. First, we look at the heat needed to warm the ice to 0 degrees C. The specific heat of ice is found in Table 9-1 on page 206 of your textbook.
Next, we determine the heat energy needed to melt the ice at 0 degrees C to water at 0 degrees C. The latent heat of melting of water is found in Table 9-2 on page 207.
The final heat value we want to know is the heat required to raise the temperature of the water from 0 degrees C to +5 degrees C.
We add these three parts together to determine the heat energy needed to convert 400 grams of -5 degree C ice to +5 degree C water.
24. A steel railroad rail is 24.4 meters long. How much does it expand during a day when the low temperature is 50 degrees F (18 degrees C) and the high temperature is 100 degrees F (38 degrees C)?
We need the coefficient of thermal expansion for steel to find the change in length. This is found on page 215 of your textbook.
