The second law of thermodynamics in terms of entropy can be stated as every physical or chemical process in nature takes place in such a ways so as to increase the entropy of the system.
$$i.e., dS \geq 0$$
Entropy defines disorderness in the system. It remains constant in the reversible process and always increases in the irreversible process.
From 2nd law , dQ = TdS
From 1st law , dU = dQ - PdV
$$ dU = TdS - PdV $$ This is the expression for 1st law in terms of entropy.
The 1st law of thermodynamics does not indicate the thermodynamic process and the amount of heat energy converted to the mechanical work. These terms are explained in the 2nd law of thermodynamics. This is the significant difference between the first and second law of thermodynamics.
In diesel engine, the air can be compressed adiabatically such that its temperature reaches about 700° C before mixing the diesel with air in the cylinder. This temperature is quite enough to ignite the diesel. Hence spark plug is not necessary in a diesel engine.
Heat engine is a device that converts heat energy into mechanical work and its efficiency is , $$\eta = (1-\frac{Q_2}{Q_1})$$ where Q2 is the heat rejected to the sink and Q1 is the heat supplied. Since Q2 < Q1, the efficiency is always less than unity. Hence the efficiency of an engine can never be 100%. Thus there is loss of energy as thermal pollution. So, it is not possible to construct a heat engine that creates no thermal pollution.
The second law of thermodynamics can be stated in two ways:
Kelvin Statement
It is impossible to get a continuous supply of work from a body by cooling It to a temperature lower than the coldest of its surroundings.
Clausius Statement
It is impossible for a self-acting machines unaided by any external agency to transfer heat from a body at lower temperature to a body at higher temperature.