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QUIZ_1v2+Solution

# QUIZ_1v2+Solution - b What is the relative change in volume...

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QUIZ #1 – 20 minutes Jan. 30, 2012 Name : ___SOLUTION ___________________________________ A balloon filled with 1 mole of an ideal gas is moved from the ground surface, where the pressure is 1 atm and the temperature is 25ºC, to a higher altitude where the pressure is 0.5 atm and the temperature is also 25ºC. Suppose this move is done reversibly and isothermally . Calculate the thermodynamic properties listed below. You are given that R = 8.314 J mol -1 K -1 = 0.0821 L atm mol -1 K -1 . Also, remember that T in Kelvin = T in Celsius + 273.15 Please, properly justify your answers! a) If the system consists of the gas in the balloon, is this an open, closed or isolated system, and why? Clearly system exchanges no material with the surroundings so it must be closed or isolated. Also, because ΔT = 0, ΔE = 0 = q + w. We have a change in volume, so w≠0 and therefore q≠0 and the system exchanges heat with the surroundings. Therefore system is closed.
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Unformatted text preview: b) What is the relative change in volume of the system (in other words, what is V 2 /V 1 )? Ideal gas law: P 1 V 1 = nRT = P 2 V 2 since n and T are constant Therefore P 1 V 1 = P 2 V 2 and V 2 /V 1 = P 1 /P 2 = 1 atm / 0.5 atm = 2 c) What is ΔE in Joules? ΔE = C v ΔT = 0 because ΔT = 0 d) What is ΔH in Joules? ΔH = C p ΔT = 0 because ΔT = 0 e) What is Δ(PV) in Joules? Δ(PV) = Δ(nRT) = nR Δ(T) = 0 because ΔT = 0 f) What is w in Joules? w = - ∫ p dV = - ∫ nRT dV = -nRT ∫ dV = -nRT ln (V 2 /V 1 ) V V w = - (1 mol) (8.314 J mol-1 K-1 ) (25+273.15) K (ln 2) = -1718 J g) What is q in Joules? Which way is heat transferred (to the system or out of the system)? q = ΔE – w = 0 – (-1718 J) = +1718 J. Positive value means heat into the system. You have to show your work. No partial credit for unsubstantiated answers!...
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