Question

Which of the two curves isothermal and adiabatic is more steeper and why?

Answer 1

Slope of adiabatic curve is greater than the isothermal curve.

(Slope of adiabatic curve) /(slope of isothermal curve) =gama=C(p) /C(v)

pv = constant for isothermal process

p v^gamma = constant for adiabatic process

so, p = const. / v^gamma

differentiating both sides,

dp / dv = const (-gamma) v^(-gamma-1) = const (-gamma) / v^(gamma+1)

for isothermal dp / dv = const (-1) / v^(2) ; gamma = 1

dp / dv more for adiabatic as gamma > 1

adiabatic has greater slope in p-v diagram