For each one of the following eases below determine if the h

For each one of the following eases below determine if the heat engine satisfies the first law and if it violates the second low. Explain it. Q_H = 20,000 Btu/hr, Q_L = 0 Btu/hr, W = 20,000 Btu/hr Q_H = 20,000 Btu/hr, Q_L = 6500 Btu/hr, W = 175000 Btu/hr

Solution

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy.

Hence according to first law, Q_H = Q_L + W

For engine 1,  Q_H = 20,000 ; Q_L = 0 ; W = 20,000 . It satisfies first law.

For engine 2, Q_H = 20,000 ; Q_L = 6500 ; W = 175000 . It doesn\'t satisfy first law.

Kelvin-Planck statement of the Second Law of Thermodynamics

It is impossible to construct a cyclic heat engine that produces no other effect but the absorption of energy from a hot reservoir and the production of an equal amount of work. In other words efficiency of heat engine cannot be greater than or equal to 1. It is always less than 1.

Thermal efficiency of heat engine is given as , n = W/Q_H

for engine 1, n = 20000/20000 = 1. It violates second law.

for engine 2, n = 175000/20000 = 8.75. It violates second law.