A Carnot heat engine operates between reservoirs at 182℃ and 0℃. If the engine extracts 25 J of energy from the hot reservoir per cycle, how many cycles will it take to lift a 10 kg mass a height of 10 m?

Key Concepts

Carnot Heat Engine

A Carnot heat engine is an idealized thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two thermal reservoirs. It operates on the principles of reversible processes and is defined by the temperatures of the hot and cold reservoirs. The efficiency of a Carnot engine is given by the formula η = 1 - (T_c / T_h), where T_c and T_h are the absolute temperatures of the cold and hot reservoirs, respectively.

Work and Energy

In physics, work is defined as the energy transferred when a force is applied to an object over a distance. The work done on an object can be calculated using the formula W = F × d, where F is the force and d is the distance moved in the direction of the force. In the context of lifting a mass, the work done is equal to the gravitational potential energy gained, which can be calculated using W = m × g × h, where m is mass, g is the acceleration due to gravity, and h is the height.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the Carnot engine, the energy extracted from the hot reservoir is converted into work done on the mass being lifted. The total energy output of the engine must equal the energy input from the hot reservoir, minus any energy lost to the cold reservoir, thus allowing for the calculation of the number of cycles needed to perform a specific amount of work.