Chemistry Lost

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?

Answer 1

You must do an energy transfer balance where the heat lost by the cooling gold equals the heat gained by the warming water.  I will set this up for you, and you can do the math.  

 

T = equilibrium temperature = ?

 

T_g = initial temperature of the gold = 60°C

m_g = mass of the gold = 0.025 kg

c_g = specific heat of gold = 130 J/(kg°C)  [look it up and verify]

 

T_w = initial temperature of the water = 5°C

m_w = mass of the water = (1 g/ml)(100 ml) = 100 g = 0.100 kg

c_w = specific heat of water = 4180 J/(kg°C) [look it up and verify]

 

The energy transfer balance is

 

m_gc_g(T_g - T) = m_wc_w(T - T_w)

 

Note you now have one equation with only one unknown, which is T.  Just do the algebra to find T and plug in the numbers.  Can you finish from here?