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Secure https: session, masteringphysics.com myct/itemView? assignment ProblemID 73043465&offset; next PHYS 212 Sp17 c19 Problem 19.64 Problem 19.64 Part A 26 g of nitrogen gas at STP are adiabatically compressed to a What is the final temperature? pressure of 25 atm Express your answer with the appropriate units. A Value Units My Answers Give Up Part B What is the work done on the gas? Express your answer with the appropriate units. Wa Value Units Submit My Answers Give Up incorrect; Try Again Part C What is the heat input to the gas? Express your answer with the appropriate units. Eva Q Value Units He e previous l 12 of 12 l retum to assignment

Explanation / Answer

An ideal gas undergoing an adiabatic, reversible process satisfies the condition: pV^ = constant throughout the process. = Cp/Cv is the heat capacity ratio. For a diatomic ideal gas like nitrogen it is = (7/2)R / (5/2)R = 7/5 Using ideal gas you may rewrite adiabatic equation as: p^(-1)T^(-) = constant Hence: p^(-1) / T^ = p^(-1) / T^ => T = T (p/p)^[(-1)/] = 273.15K (25atm / 1atm)^[(7/5-1)/(7/5)] = 273.15K (22)^[2/7] = 685.2K The work done on the gas is given by the integral W = - p dV from V to V V can expressed in terms of V by adiabatic equation: pV^ = constant = pV^ => V = Vp^(1/) p^(-1/) => dV = Vp^(1/) (-1/)p^(-1/ - 1) dp => W = - p dV from V to V = - p * V*p^(1/) * (-1/)*p^(-1/ - 1) dp from p to p = V*p^(1/) * (1/) * p^(-1/) dp from p to p = V*p^(1/) * (1/) * [1/(1 - 1/)] * { p^[(1 - 1/)] - p^[(1 - 1/)] } = V*p^(1/) * [1/( - 1)] * { p^[(1 - 1/)] - p^[(1 - 1/)] } = V*p * [1/( - 1)] * { (p/p)^[(1 - 1/)] - 1 } = n*R*T * [1/( - 1)] * { (p/p)^[(1 - 1/)] - 1 } For this process W = (25g/28g/mol)*8.314472J/molK * 273.15K * (5/2) * { (25)^(2/7) -1} = 7 647.1J

Heat into the gas= amoumt of workdone=7647.1J

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