The second law of thermodynamics can also be stated using Clausius, Kelvin and Planck statements also. Each statement is based on an irreversible process.
The Clausius and the Kelvin and Planck statements of the second law of Thermodynamics are given below:
Clausius statement states “it is impossible for a self acting machine working in a cyclic process without any external force, to transfer heat from a body at a lower temperature to a body at a higher temperature. It considers transformation of heat between two heat reservoirs.
Kelvin – Planck statement:
Kelvin – Planck statement states “it is impossible to construct an engine, which is operating in a cycle produces no other effect except to external heat from a single reservoir and do equivalent amount of work.
It considers the transformation of heat into work.
Equivalence of Clausius statement to the Kelvin – Planck statement
Consider a reservoir having temperature T1 and another reservoir at temperature T2. The temperature T1 is higher than the temperature T2. Consider a heat pump which requires no work and transfers an amount of Q2 from low temperature to a higher temperature reservoir, which is violating the Clausius statement. Consider an amount of heat Q1 (greater than Q2) be transferred from higher temperature reservoir to a heat engine which develops a net work, W = Q1 – Q2 and rejects Q2 to the low temperature reservoir.
Since there is no heat interaction with the low temperature, it can be eliminated. The combined system of the heat engine and heat pump acts then like a heat engine exchanging heat with a single reservoir, which violates the Kelvin – Planck statement.