The human body has an average temperature of 37°C. A person, with a fever of 40°C, would like to know what will be the temperature of her skin in an ice bath, after reaching a steady state. Which of the following equations can be used to create an analogous formula for heat transfer due to conduction?
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Correct Answer: B. V = IR
At a first glance, one might think that none of these equations deal with heat. It is important to recall that heat is energy. Immediately one can rule out answer choices A and C, as they do not deal with energy. Taking a deeper look into equation D we can see Einstein’s famous equation states that the energy is equal to some constant squared. We can try to relate that with heat, by asking if heat is proportion to a single constant. We know that this is not true by 1.) ice melts at different rates depending on the temperature and 2.) chocolate and ice melt at different rates at the same temperature. We have parameterized heat based on ambient temperature as well as by the individual material. The remaining solution is choice B.
Lets confirm this be taking a further look into choice B. Ohm’s law says that the potential is directly related to the current by a resistance. This can be rearranged to have the current indirectly related to the potential through resistance, or directly related to the potential through the conductance, g.
The current is a charge rate, Q/t. If we replace charge with heat, we can obtain the thermal conduction formula. With the charge rate becoming a heat rate, the conductance becoming a heat conductance, and the potential difference becoming the temperature drop.
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