A mercury-in-glass thermometer is calibrated. The lengths of the mercury thread at the upper and lower fixed points (100°C and 0°C) are 24.0 cm and 4.0 cm respectively.
(a) The thermometer is then immersed in a beaker of water at room temperature. It is found that the length of the mercury thread is 9.0 cm. Find the room temperature.
(b) A metal cube at 80°C is immersed into the beaker of water. The thermometer in (a) is then immersed in the water. The length of mercury thread keeps increasing until it becomes steady at 9.4 cm.
(i) What is the final temperature of the water-metal system?
(ii) Given that the mass of water is 1 kg and the specific heat capacity of water is 4200 J kg-1 K-1, calculate the heat capacity of the metal.
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Answer:
(a) t/100 = (9 - 4) / (24 - 4)
t = 5 / 20 * 100
t = 25 °C
(b)
(i) t/100 = (9.4 - 4) / (24 - 4)
t = 5.4 / 20 * 100
t = 27 °C
(ii) Heat gained by water = heat loss by metal
Using Q = mcΔθ for water, and Q = CΔθ for the metal (c is specific heat capacity, C is heat capacity),
(mwater) (cwater) Δθwater = (Cmetal) Δθmetal
(1)(4200)(2) = (Cmetal) (80 - 27)
Cmetal = 8400 / 53
Cmetal = 158.5 J K-1
