PROGRAM DESCRIPTION A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The most efficient heat engine is the Carnot engine, where the Carnot efficiency is given by the relation Th- T Th where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir, both given in Kelvin, K. Hot reservyoir Cold reservoir Now, suppose we know the current efficiency of the Carnot engine and want to know how much the temperature of the hot reservoir must increase to increase the efficiency to a certain amount, given the constant temperature of the cold reservoir. We can then manipulate the Carnot efficiency equation to solve for the difference in the temperature of the hot reservoir as follows: 1-72 1-1 where 1 is the original efficiency and 2 is the increased efficiency For example, suppose a Carnot engine operates with efficiency of 40%. How much must the temperature of the hot reservoir increase, so that the efficiency increases to 50%, assuming that the temperature of the cold reservoir remains at 9 C? Since we know the original and increased Carnot efficiencies as well as the temperature of the cold reservoir, we can solve the problem, but first we need to convert the values to the appropriate units. The percentage values can simply be converted to their decimal equivalents and then the temperature of the cold reservoir in Celsius can be converted to Kelvin with the following formula: TxToc 273.15