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Unformatted text preview: ange: U23 = nCV T = n8R T = (1.00 mol)8(8.315 J/mol K)(231 K 389 K) = 1.97 103 J; heat flow added to the gas, from the first law of thermodynamics: U23 = Q23 W23; 1.97 103 J = Q23 ( 1.31 103 J), which gives Q23 = 3.28 103 J. For the constant volume process, 3 1, we have work done by the gas: W31 = P V = 0; internal energy change: U31 = nCV T = n8R T = (1.00 mol)8(8.315 J/mol K)(550 K 231 K) = + 3.98 10 3 J; heat flow added to the gas, from the first law of thermodynamics: U31 = Q31 W31; + 3.98 103 J = Q31 0, which gives Q31 = + 3.98 103 J. (d) For the complete cycle, we have Wcycle = W12 + W23 + W31 = + 2.01 103 J + ( 1.31 103 J) + 0 = + 0.70 103 J. Qcycle = Q12 + Q23 + Q31 = 0 + ( 3.28 103 J) + 3.98 103 J = + 0.70 103 J. Ucycle = U12 + U23 + U31 = 2.01 103 J + ( 1.97 103 J) + 3.98 103 J = 0. 19.84
From the ideal gas equation, for the isothermal compression, we have: P2V2/P1V1 = (P2/P1)(V2/V1) = T2/T1 ; (P2/1.00 atm)(1/5) = 1, which gives P2 = 5.00 atm. For the adiabatic expansion we have P2V2 = P3V3, or P2 /P3 = (V3/V2); (5.00 atm/P3) = (5)5/3, which gives P3 = 0.342 atm. If we compare the initial and final states, from the ideal gas equation we have: P1V1/P3V3 = (P1/P3)(V1/V3) = T1/T3 ; (1.00 atm/0.342 atm)(1) = 273 K/T3 , which gives T3 = 93 K. Thus we have Thigh = 273 K, Tlow = 93 K, Phigh = 5.00 atm, Plow = 0.342 atm. 19.86
(a) We find the power radiated from Q/t = eAT4 = (1.0)(5.67 108 W/m2 K4)4(7.0 108 m)2(5500 K)4 = 3.2 1026 W. (b) Because this radiation passes through a sphere centered at the Sun, we have P/4R2 = (3.2 1026 W)/4(1.5 1011 m)2 = 1.1 103 W/m2. Physics 7B Fall, 2006 Homework 1 Solutions
17.8
At any temperature below 20C the expansion cracks will increase. Thus the expansion from 20C to 50C must eliminate the cracks. Any higher temperature will cause stress in the concrete. If the cracks have a width L, we have L = L0 T = [12 106 (C)1](12 m)(50C 20C) = 4.3 103 m = 0.43 cm. 17.14
(a) The expansion of the container causes the enclosed volume to increase as if it were made of the s...
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 Fall '08
 Packard
 Heat

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