question for temperature and heat

• Change each of the following to the Celsius and Kelvin scales: 68 ͦ F, 5 ͦ F ,176 ͦ F
Tc = ³/9 (tF – 32); Tk = tc + 273.15 = tc + 273. then
tF = 68 ͦ F = tc = 20 ͦ C = Tk = 293 K
tF = 5 ͦF = tc = -15 ͦ C = Tk = 258 K
tF = 176 ͦF= tc = 80 ͦ C = Tk = 352 K


• Hydrogen may be liquefied at – 235 ͦ C under a pressure of 20 atm. What is the temperature on the Fahrenheit scale?
tF = 1.8tc + 32 = 1.8 (-235) + 32 = -391 ͦ F


• The temperature of liquid hydrogen is 20 K. what is the temperature on the Fahrenheit scale?
20 K = 20 – 273 = -253 ͦ C
tF = 1.8tc + 32 = 1.8(-253) + 32 = - 423 ͦF



• Compute the increase in length of 50m of cooper wire when its temperature changes from 12 to 32 ͦC.
∆L = αLo ∆T = (1.67 x 10-³ ͦ C-1)(50m)(20 ͦ C) = 16.7mm.


• A rod 3m long is found to have expanded 0.091cm length for a temperature rise of 60 ͦC. what is α for the material of the rod?

α= 1 /Lo = ∆L /∆T = 0.091 x 10^ -2 m / (3m)(60K) = 5.1 x 10 -6 K^-1



• A brass rod is 0.70m long at 40 o C. fined the length of this rod at 50 ͦ C.
L = Lo (1 + α∆T) = (0.70m){1 + (19.3 x 10^ -6 / ͦ C)}. L = 0.70013 m.



• A block of concrete has a cross section of 10 m2 and the thickness of 0.10m. one side is at 40 ͦ C, and the order is at 20 ͦ C. what is the rate of heat transfer?
Q = k . A (Thot – Tcold / d)
= (1.7 Wm-1K^-1) . (10m^2) . (40 ͦ C – 20 ͦ C / 0.10m)
= 3400 W.



• How much heat is required to raise the temperature of 400kg of mercury from
40 ͦ C to 100 ͦ C?
Q = m.c.∆T = m.c.(Tfinal – Tinitial)
= (0.4kg)(140J/kg ͦ C)(100-40) ͦ C = 3360 J.



• Deep bore holes into the earth show that the temperature increases about 1 ͦ C for each 30m of depth. If the earth’s crust has a thermal conductivity of about 0.80 W/ ͦ C .m, how much heat flows out through the surface of the earth second for each square meter of surface area?
:: One has ∆Q / ∆T = kA (∆T / ∆x).
then ∆Q / ∆t = (0.80W/m . k)(1m2)(1 K/30m)= 27 mW/m2.



• A very small hole in an electric furnace used treating metals acts nearly as a blackbody. If the hole has an area 100mm2, and it is desired to maintain the metal at 1100 ͦ C, how much power travels through the hole?
Power = σAT4 = (3.67 x 10^-8)(10^-4)(1373.15)4 = 20.2 W.