\prob{14}
The total energy of a blackbody radiation source is collected for one minute and used to heat water. The temperature of the water increases from 20.0 degrees Celsius to 20.5 degrees Celsius. If the absolute temperature of the blackbody were doubled and the experiment repeated, which of the following statements would be most nearly correct?
 The temperature of the water would increase from 20 degrees Celsius to a final temperature of 21 degrees Celsius.
 The temperature of the water would increase from 20 degrees Celsius to a final temperature of 24 degrees Celsius.
 The temperature of the water would increase from 20 degrees Celsius to a final temperature of 28 degrees Celsius.
 The temperature of the water would increase from 20 degrees Celsius to a final temperature of 36 degrees Celsius.
 The water would boil within the oneminute time period

Statistical Mechanics}Blackbody Radiation Formula
Recall
where is the power and the energy and the temperature.
So, initially, the blackbody radiation emits . When its temperature is doubled, it emits .
Recall that water heats according to . So, initially, the heat gain in the water is . Finally, , where is the unknown change in temperature.
Conservation of energy in each step requires that and , i.e., that . Divide the two to get . Assuming the experiment is repeated from the same initial temperature, this would bring the initial to , as in choice (C).
