A 400-g piece at water at 120.0 degree C is dropped into a cup containing 450g o

Question

A 400-g piece at water at 120.0 degree C is dropped into a cup containing 450g of water at 15.0 degree C. The final temperature of the system is measured to be 40.0 degree CC. Calculate the specific heat of the metal, assuming no heat is exchanged with the surroundings or the cup. The specific heat of water is 4190 J/(kg.K). (1) 2830 J/(kg.K) (2) 1470 J/(kg.K) (3) 342 0 J/(kg.K) (4) 3780 J/(kg.K) (5) None of the above Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10 degree C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300g of water at 20 degree C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0 degree C. In the second run, an identical cube of alcohol is added to 500g of water at 20 degree C and the temperature at thermal equilibrium is 10 degree C. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The heat of fusion of the alcohol is closest to (1) 5.5 times 10^4 J/kg (2) 7.1 times 10^4 J/kg (3) 6.3 times 10^4 J/kg (4) 8.7 times 10^4 J/kg (5) None of the above. At what temperature would the root-mean-square speed (thermal speed) of oxygen molecules be 13.0m/s?

Explanation / Answer

Mass of metal m = 400 g

= 0.4 kg

Initial temperature of the metal t = 120 o C

Mass of water M = 450 g = 0.45 kg

Initial temperature of the water t ' = 15 o C

Final tempearture of the system T = 40o C

Specific heat of water C = 4190 J / kg o K

Heat lost by metal = Heat gain by water

mc( t - T ) = MC(T-t ' )

0.4(c)(120-40) = (0.45)(4190)(40-15)

32c = 47137.5

c = 1473 J / kg K

= 1470 J/kg K ( three significant figures)

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