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Chapter 13

Chapter 13. A highway is made of concrete slabs that are 15 m long at 20C. The temperature range for the road is -20 to +40C. a) What is the minimum size of the expansion gap at 20C b) What is the size of the expansion gap when it is -20C?. D L = L a D T = (15) (12x10 -6 ) (20)

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Chapter 13

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  1. Chapter 13 A highway is made of concrete slabs that are 15 m long at 20C. The temperature range for the road is -20 to +40C. a) What is the minimum size of the expansion gap at 20C b) What is the size of the expansion gap when it is -20C? DL = L aDT = (15) (12x10-6) (20) = 3.6 mm DL = L aDT = (15) (12x10-6) (60) = 10.8 mm

  2. Chapter 13 An ideal gas that occupies 1.2m3 at a pressure of 105 Pa and a temperature of 27C is compressed to 0.6 m3 and heated to 227C. What is the new pressure? PV = n R T P1 V1 / T1 = n R P2 V2 / T2 = n R P1 V1 / T1 = P2 V2 / T2 P2 = P1 ( V1/V2) (T2/T1) = 105 ( 1.2/0.6) ( 273+227)/(273+27) = 3.3 x 105

  3. Chapter 13 What is the temperature of an ideal gas whose molecules in random motion have an average translational internal energy of 3.20x10-20 J U = (3/2) k T T = (2/3) U/k = (2/3) (3.2x10-20)/(1.38x10-23) = 1546 K

  4. Chapter 14 How much heat is required to change 1 Kg of ice at -20C into steam at 110C. (note Cice = 0.5 kcal/(Kg K) CH20 = 1 kcal/(Kg K) Lf = 79 kcal/Kg, Lv = 539 kcal/Kg) Q = CiceDTiceM + Lf M + CwaterDTwater M + LV M + CsteamDTsteamM = (0.5) (0- -20) + 79 + 1 (100-0) + 539 + 0.5(110 – 100) = 733

  5. Chapter 14 For a temperature difference of 20C, a slab of material conducts 10 W/m2 ; another of the same shape conducts 20 W/m2. What is the rate of heat flow through both slabs placed next to each other, with a temperature difference of 20C. I = kADT / d = DT / R R = DT /I R1 = DT /I1 = 20/10 = 2 C m2 / W R2 = DT /I2 = 20/20 = 1 C m2 / W R12 = R1 + R2 = 3 C m2 / W I12 = DT / R12 = 20 / 3 = 6.67 W/m2

  6. P V Chapter 15 A monatomic ideal gas at 27C undergoes a constant volume process, and then a constant pressure process as shown. During this it changes from 1 liter at 2 ATM to 2L at 1 ATM a) What is the work done by the gas. b) What is the final temperature of the gas? 1 W = PDV W12 = 0 W23 = (1x105 )(10-3) = 100 J 2 3 PV = n R T P1 V1 / T1 = n R P2 V2 / T2 = n R P1 V1 / T1 = P2 V2 / T2 T2 = T1 ( V2/V1) (T1/T2) = T1 ( 2/1) (1/2) = T1

  7. Chapter 15 An engine releases 0.45kJ of heat for every 0.1 kJ of work it does. a) What is the efficiency of the engine? b) If the waste heat is expelled at room temperature (300K), what is the minimum temperature TH that the heat is input? e = W / QH = W / (W + Qc) = 0.1 / (0.1 + 0.45) = 0.18 e < 1 - TC / TH Carnot is maximum efficiency Tc/TH < 1-e Tc/ (1-e) < TH TH > Tc / (1-e) > 300 / (1 - .18) > 366

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