Brass is an alloy made from copper and zinc. A 0.59 kg brass sample at 90.0 C is dropped into 2.80 kg of water at 5.0 C. If the equilibrium temperature is 6.8C, what is the specific heat capacity of brass?

Since no heat is lost to the surroundings, the change in thermal energy of the brass piece and the water sample have have the same magnitude:

m_brass ∙ c_brass ∙ ∆T_brass = m_water ∙ c_water ∙ ∆T_water

=>

c_brass = c_water ∙ (m_water/m_brass) ∙ (∆T_water/∆T_brass)

= 4186J/kg°C ∙ (2.8kg/0.59kg) ∙ ((6.8°C - 5°C) / (98°C - 6.8°C))

= 392J/kg