A diatomic ideal gas at pressure P 1 and volume V 1 is expanded reversibly and adiabatically until its RMS speed falls to one-third of its initial value. It is then compressed isothermally to a volume

Question

A diatomic ideal gas at pressure P 1 and volume V 1 is expanded reversibly and adiabatically until its RMS speed falls to one-third of its initial value. It is then compressed isothermally to a volume V 1 /2. The final pressure is

TestHub · Accepted Answer

u rms ∝ √(T), so T 2 = T 1 /9 after the adiabatic step (this needs V 2 /V 1 = 9 2.5 = 243 but the intermediate volume is not needed). The isothermal step keeps T 3 = T 1 /9. From P = nRT/V: (P 3 )/(P 1 ) = (T 3 )/(T 1 )·(V 1 )/(V 3 ) = 1/9× 2 = 2/9. Matches (a).

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