Question

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

Answer 1

mass of the nugget m_n = 25g

Initial temperature of nugget T₁ = 60^oC

Final temperature of the nugget T

volume of water V = 100ml

density of water = 1g/cc = 1g/ml

mass of the water m_w= V*1 = 100g

Initial temperature of water T₂ = 5^oC

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

m_nc_n(T₁ - T) = m_wc_w(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 = 5.42^oC

Therefore the final temperature = 5.42^oC