State the first law of thermodynamics in words and show how this relates heat flow work and internal energy. write down an equation that describes this law and state the sign convention for work b. describe what is meant by a heat engine and use a sketch to show the principle of operation for such a device. give one example of a heat engine that is commonly encountered in industry c. you've been asked to design a heat engine that can operate with a theoretical carnot efficiency of at least 25% when the temperature of the cold reservoir is fixed at 50°c. calculate the minimum temperature needed for the hot reservoir to achieve this d. when you construct this device, you find that the actual efficiency is only 15 %. explain why this efficiency is lower than the theoretical limit and what the most likely source of further inefficiency is. e. a heat pump uses 300j of work to pump 200j of heat from the low temperature reservoir to a high temperature reservoir. how much heat is delivered to the high temperature reservoir?