Thermal Fun!

Classical Mechanics Level 3

Find the minimum attainable pressure of an ideal gas in the process $T={ T }_{ 0 }^{ }+\alpha { V }^{ 2 }$ , where ${T}_{0}$ and $\alpha$ are positive constants and $V$ is the volume of one mole of gas.

If ${ P }_{ min }$ is in the form $\delta R\sqrt { \alpha { T }_{ 0 } }$ , find $\delta$ .

R is the Universal gas constant.

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2 solutions

Prince Loomba
Apr 2, 2016

Replace v by nrt/p. Make the discriminant of the obtained quadratic in t>=0 to get minimum p.

Vignesh Sankar
Mar 5, 2016

Given, T=T0+aV^2;-------------------------------------------------------------(1) Ideal Gas (PV=RT);--------------------------------------------------(2) Soln: Rearranging the Ideal Gas Eqn., P=R(T/V)-----------------------(3) which implies that min P is attained at min (T/V). Divide (1) by V, we get (T/V)=(T0/V)+aV; Differentiating the above eqn w.r.t V and equating to zero for min (T/V),we get, (T/V)min = 2 sqrt (aT0)----------------------------------------------(4) Substitute (4) in (3),we get, Pmin = 2R sqrt (aT0)

Thermal Fun!

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