A sample of ideal gas expands from an initial pressure and volume of 31.1 atm an

Question

A sample of ideal gas expands from an initial pressure and volume of 31.1 atm and 1.71 L to a final volume of 7.27 L. The initial temperature is 309 K. If the gas is monatomic and the expansion isothermal, what are the (a) final pressure pf, (b) final temperature Tf, and (c) work W done by the gas? If the gas is monatomic and the expansion adiabatic, what are (d)pf, (e)Tf, and (f)W? If the gas is diatomic and the expansion adiabatic, what are (g)pf, (h)Tf, and (i)W?
Give temperatures in kelvins.

Explanation / Answer

PART 1 isothermal final temperature will remain same T(final)=309K isothermal implies P*V=constant 31.1*1.71=7.27*P P=7.31atm work done by gas=n*R*T*ln(V2/V1) n*R*T=31.1*1.71(PV=nRT) work=53.181*ln(7.27/1.71) =76.96 PART 2 adiabatic P*V^(GAMMA)=constant mono-atomic GAMMA=5/3 P*(7.27)^(5/3)=31.1*(1.71)^(5/3) P=31.1*(1.71/7.27)^(5/3) P=2.78 atm similarly for temperature use T*V^(GAMMA-1)=constant T*(7.27)^(5/3-1)=309*(1.71)^(5/3-1) T=309*(1.71/7.27)^(2/3) T=117.74K work done =change in internal energy =n*(cv)*change in temperature cv=HEAt capacity at constant volume when GAMMA is given cv can be easily calculated where n can be calculated using ideal gas equation PV=nrt Same procedure can be applied for dia atomic gas just replace initial GAMMA by 7/5

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