Question : Show that an adiabatic curve is always stepped that an isothermal curve?
Doubt by Niyati
Solution :
As we know, that adiabatic and isothermal curve are drawn between pressure (P) and volume (V) so their slope will be given by dP/dV.
Solution :
As we know, that adiabatic and isothermal curve are drawn between pressure (P) and volume (V) so their slope will be given by dP/dV.
In an isothermal process,
PV = const.
PV = const.
differentiating both sides
In an adiabatic process,
PVγ = cont.
differentiating both sides
From equation (1) and equation (2)
Slope of Adiabatic curve = γ×Slope of Isothermal Curve
Slope of Adiabatic curve = γ×Slope of Isothermal Curve
where γ is the ratio of two specific heats (Cp/Cv) which is always greater than 1.
Hence, We have proved that adiabatic curve is always steeper than the isothermal curve.
Hence, We have proved that adiabatic curve is always steeper than the isothermal curve.