A 25 g gold nugget with an initial temperature of 60 °C is dropped into an insulated cup containing 100 ml of water initially at a temperature of 5°C. What is the final temperature after thermal equilibrium is established?
Table 3.4 Specific Heat Capacities of Some Common Substances Substance Specific Heat Capacity (J/g °C) Lead 0.128 Gold 0.128 Silver 0.235 Copper 0.385 Iron 0.449 Aluminum 0.903 Ethanol 2.42 Water 4.184
mass of the nugget mn = 25g
Initial temperature of nugget T1 = 60oC
Final temperature of the nugget T
volume of water V = 100ml
density of water = 1g/cc = 1g/ml
mass of the water mw= V*1 = 100g
Initial temperature of water T2 = 5oC
Final temperature of water = T
since the thermal equilibrium is reached between the nugget and the water, the final temperatures of both are the same.
heat lost by the gold nugget = heat gained by the water
mncn(T1 - T) = mwcw(T - T2)
25*0.128*(60 - T) = 100*4.184*(T - 5)
=> 60 - T = 130.75(T - 5)
=> 60 - T = 130.75T - 653.75
=> 131.75T = 713.75
=> T = 5.4174 = 5.42oC
Therefore the final temperature = 5.42oC
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