Physics

Problem

For an ideal gas, reversible isothermal and reversible adiabatic processes are described by the relations

PV=\text{constant}

and

PV^{\gamma}=\text{constant}

respectively, where

\gamma>1

. a. (i) Starting from the respective relations, obtain an expression for the slope

\left(\dfrac{dP}{dV}\right)

of each curve on a

P\text{–}V

diagram in terms of

P

and

V

at an arbitrary point on the curve. b. (ii) Show that, for the same values of

P

and

V

, the magnitude of the slope for the adiabatic curve exceeds that for the isothermal curve by a factor of

\gamma

. c. (iii) Hence explain, with physical reasoning based on the First Law of Thermodynamics, why the adiabatic curve is qualitatively steeper than the isothermal curve throughout the diagram.

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