explain why B and C represent isothermal and adiabatic process respectively ?

Dear Student,

Isothermal and adiabatic curves are identifies by the slope of the curve. Slope of adibatic curve on PV diagram is greater than the slope of isothermal curve. 
In the given graph, we can see that slope of C is greater than B, therefore C represents adiabatic process while B represents isothermal process. 

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