For one mole of an ideal gas, find the maximum attainable temperature for: (a) p=p₀-αV² and (b) p=p₀exp(-βV), where p₀, α and β are positive constants.
Options

Question

For one mole of an ideal gas, find the maximum attainable temperature for: (a) p=p₀−αV² and (b) p=p₀exp(−βV), where p₀, α and β are positive constants.

G1 Physics · Accepted Answer

Use PV=nRT, U=(f/2)nRT, γ=1+2/f and vᵣₘₛ=√(3RT/M). At the same temperature, average translational kinetic energy depends only on T. Evaluating the given data/statements gives Tₘₐₓ=(2/3)(p₀/R)√(p₀/(3α)); Tₘₐₓ=p₀/(eβR). Therefore the correct answer is A.