A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature (V0$$, $$T0). From the details given in the graph, find the value of adiabatic constant γ

Question

A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature (V0$$, $$T0). From the details given in the graph, find the value of adiabatic constant γ

Infinity Learn · Accepted Answer

We have, for an adiabatic process, in relation with temperature and volumeTVγ$$-1$$ $$=$$ constantDifferentiating with respect to T.Vγ$$-1.1$$ $$+$$ T.$$($$γ$$-1)V$$γ$$-2dVdT$$ $$=$$ $$0dVdT$$ $$=$$ $$VT($$γ$$-1)But$$ from the graph $$dVdT(T0$$,$$V0)=$$ $$tan$$$$($$π$$-$$θ$$)$$ $$=$$ $$-$$$$tan$$ θ$$V0T0($$γ$$-1)$$ $$=$$ $$tan$$ θ ⇒ γ$$-1$$ $$=$$ $$V0T0tan$$ θγ $$=$$ $$V0T0tan$$ θ$$+1$$

A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature $(V_{0}, T_{0})$ . From the details given in the graph, find the value of adiabatic constant $γ$

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A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature (V0, T0). From the details given in the graph, find the value of adiabatic constant γ

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A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature $(V_{0}, T_{0})$ . From the details given in the graph, find the value of adiabatic constant $γ$