State second law of thermodynamics. How is heat engine is different from a refrigerator?

Second law consists of two statements
1) Kelvin–planck statement: It is impossible to construct any machine to transfer total heat energy into work.
2) Claussius statement: Heat can not flow from a cold body to hot body by itself.
3) Heat engine: A device which converts heat energy into work is called heat engine.

Block diagram of heat engine:
The essential parts of the heat engine are
1) Source : It is a body at higher temperature T₁K. Heat (Q₁) is taken from the source.
2) Working substance : In steam engine the working substance is steam. In diesel engine the working substance is mixture of fuel and air.
3) Sink : It is a body at lower temperature. It absorbs heat (Q₂) rejected by the working substance.
Efficiency : The ratio of workdone by the engine to the amount of heat absorbed (Q₁) is called efficiency.
$\mathrm{\eta }=\frac{\mathrm{W}}{{\mathrm{Q}}_1}=\frac{{\mathrm{Q}}_1-{\mathrm{Q}}_2}{{\mathrm{Q}}_1}=1-\frac{{\mathrm{Q}}_2}{{\mathrm{Q}}_1}\text{ (or) }\mathrm{\eta }=1-\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}$
Refrigerator: The refrigerator is the heat engine working in the backward direction.

In refrigerator the working substance absorbs (Q₂) amount of heat from the sink and external work done (W) is done on the working substance and finally amount of heat (Q₁) is rejected to the source.
Efficiency of the refrigerator is called coefficient of performance ($\mathrm{\beta }$) of the refrigerator.
$\mathrm{\beta }=\frac{{\mathrm{Q}}_2}{\mathrm{W}}=\frac{{\mathrm{Q}}_2}{{\mathrm{Q}}_1-{\mathrm{Q}}_2}=\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1-{\mathrm{T}}_2}$