Sm1 50thru1 51

PROBLEM 1.50 First convert temperatures from °C to K by rearranging Eq. 1.17 to solve for temperature in K T(°C) = T(K) - 273.15 → T(K) = T(°C) + 273.15 For summer: T_summer(K) = 19.5°C + 273.15 = 292.65 K For winter: T_winter(K) = -4.9°C + 273.15 = 268.25 K Next apply Eq. 1.16 to solve for temperatures in °R T(°R) = 1.8T(K) For summer: T_summer(°R) = (1.8)(292.65 K) = 526.77 °R For winter: T_winter(°R) = (1.8)(268.25 K) = 482.85°R Finally, apply Eq. 1.18 to solve for temperatures in °F T(°F) = T(°R) - 459.67 For summer: T_summer(°F) = 526.77 °R - 459.67 = 67.10 °F For winter: T_winter(°F) = 482.85°R - 459.67 = 23.18 °F PROBLEM 1.51 Use the following equations to convert from °F to °C and then to K T(°F) = 1.8 x T(°C) + 32 (1.19) T(°C) = (T(°F) - 32) / 1.8 = (T(°F) - 17.78) / 1.8 T(°C) = T(K) - 273.15 (1.17) T(K) = T(°C) + 273.15 (a) 86°F T(°C) = (86 - 32) / 1.8 = 17.78 = 30°C T(K) = 30 + 273.15 = 303.15 K (b) -22°F T(°C) = (-22 - 32) / 1.8 = -17.78 = -30°C T(K) = -30 + 273.15 = 243.15 K (c) 50°F T(°C) = (50 - 32) / 1.8 = 10°C T(K) = 10 + 273.15 = 283.15 K (d) -40°F T(°C) = (-40 - 32) / 1.8 = -17.78 = -40°C T(K) = -40 + 273.15 = 233.15 K (e) 32°F T(°C) = (32 - 32) / 1.8 = -17.78 = 0°C T(K) = 0 + 273.15 = 273.15 K (f) -459.67°F T(°C) = (-459.67 - 32) / 1.8 = -17.78 = -273.15°C T(K) = -273.15 + 273.15 = 0 K