Question

What machine is used to determine the calories in food, as well as the average heat yield from burning various grades of coal and oil?

Answer 1

calorimeter

Though not particularly beautiful machines, calorimeters are incredibly useful ones. They are used to determine the calories  food energy  in food, as well as the average heat yield from burning various grades of coal and oil. The price of coal is often dependent on the heat yield from samples burned in a calorimeter.