The heat capacity of a material can be determined by bringing it into thermal co
ID: 1836269 • Letter: T
Question
The heat capacity of a material can be determined by bringing it into thermal contact with another material of known heat capacity. For example, imagine that a piece of metal is placed in boiling water (100degreeC) and then quickly transferred into a Styrofoam cup containing 250g of water at 20degreeC. Sometime later the temperature of the water is measured to be 24degreeC. Take the heat capacity of 1 mol of water to be 75 JK^-1 and independent of temperature. Ignore any heat transfer to the environment or the cup. (a) Calculate the heat gained by the water. (b) Hence determine the heat capcity of the metal (assume it to be independent of temperature). (c) The metal has mass 100 g. What is its specific heat capacity? How does this compare with water?Explanation / Answer
Heat capacity of 1 mole of water = 75 J / K
Mass of 1 mole water M = 18 g
So, heat capacity of 18 g of water = 75 J / K
(a). mass of the water m = 250 g
Number of moles of water in mass m is n = m/M
n = 250 /18
= 13.8888 mol
temprature raise dt = 24 o C - 20 o C = 4 o C
Therefore heat gained by the water to raise the temprature by 4 o C or 4 K is Q = n (75 J/K) dt
Q = 13.88888x75x 4
= 4166.66 J
(b). temprature fall by metal dt ' = 100 o C - 24 o C = 76 o C = 76 K
Heat capacity of metal = Q / dt '
= 4166.66 / 76
Q ' = 54.82 J/K
(c). mass of metal m ' = 100 g
Specific heat capacity of metal C = Q ' / m
= 0.5482 J / g K
Specific Heat capacity of metal / Specific heat capacity of water = (0.5482 J / g K ) /(75 J / mol K )
= (0.5482 J/ g K ) /( 75 J / 18 g K )
= (0.5482 J/ g K) /(4.1666 J / g K )
= 0.1315
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