At the same point on a – diagram for an ideal gas

PHYSICS · Single correct · A Level · Physics · Engineering physics · Engineering physics

Problem

At the same point (P,V)(P,V) on a P ⁣P\!– ⁣V\!V diagram for an ideal gas, how does the slope ∣dPdV∣\left|\dfrac{dP}{dV}\right| of the adiabatic curve compare with that of the isothermal curve? (a) ∣dPdV∣adiabatic=γ ∣dPdV∣isothermal  (γ>1)\left|\dfrac{dP}{dV}\right|_{\text{adiabatic}}=\gamma\,\left|\dfrac{dP}{dV}\right|_{\text{isothermal}}\;(\gamma>1) (b) ∣dPdV∣adiabatic=∣dPdV∣isothermal\left|\dfrac{dP}{dV}\right|_{\text{adiabatic}}=\left|\dfrac{dP}{dV}\right|_{\text{isothermal}} (c) ∣dPdV∣adiabatic=1γ ∣dPdV∣isothermal  (γ>1)\left|\dfrac{dP}{dV}\right|_{\text{adiabatic}}=\dfrac{1}{\gamma}\,\left|\dfrac{dP}{dV}\right|_{\text{isothermal}}\;(\gamma>1) (d) ∣dPdV∣adiabatic=γ2 ∣dPdV∣isothermal\left|\dfrac{dP}{dV}\right|_{\text{adiabatic}}=\gamma^{2}\,\left|\dfrac{dP}{dV}\right|_{\text{isothermal}}

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