Question

A 260 g piece of brass at 95C is placed into 500 g of water at 25C in an insulated container. Calculate the final equilibrium temperature (heat) of the brass in the insulated container

Answer 1

Assume no heat loss to the surroundings and use c_brass = 0.380 J/g·°C, c_water = 4.18 J/g·°C.

Heat lost by brass = heat gained by water:
m_brass c_brass (95 − Tf) = m_water c_water (Tf − 25)

Solve for Tf:
Tf = (m_brass c_brass ·95 + m_water c_water ·25) / (m_brass c_brass + m_water c_water)

Plug numbers (m_brass = 260 g, m_water = 500 g):
m_brass c_brass = 260·0.380 = 98.8 J/°C
m_water c_water = 500·4.18 = 2090 J/°C

Tf = (98.8·95 + 2090·25) / (98.8 + 2090)
= (9,386 + 52,250) / 2,188.8
≈ 61,636 / 2,188.8
≈ 28.2 °C

Final equilibrium temperature ≈ 28.2 °C.