CSCE 1030: Homework Assignment 1 Due: 11:59 PM on Friday, February 02, 2020 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 where, Ty: the temperature of the hot reservoir in Kelvin K To: the temperature of the cold reservoir in Kelvin, K 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: where, 7: the original efficiency n2: the increased efficiency For example, suppose a Camot 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 9C? 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