The slope of isothermal and adiabatic curves are related as

Options

A. Isothermal curve slope = adiabatic curve slope
B. Isothermal curve slope = `gamma xx` adiabatic curve slope
C. Adiabatic curve slope = `gamma xx` isothermal curve slope
D. Adiabatic curve slope = `1//2 xx` isothermal curve slope

Answer

C

Explanation

For Isothermal process PV = constant
`implies PdV+VdP=0 implies (dP)/(dV)=(-P)/(V)` = `"(Slope)"_("iso")`
For adiabatic `PV^(gamma)` = constant
`implies P gamma V^(gamma-1) dV+V^(gamma)dP=0`
`implies (dP)/(dV)=(-gamma P)/(V) ="(slope)"_("adiabatic")`