Chemistry · Simulator 028
Drop a hot block of metal into cool water in an insulated cup. Choose the material, the masses and the starting temperatures, predict the final temperature, then watch heat flow from hot to cold until both meet.
In an insulated calorimeter, heat lost by the hot object equals heat gained by the cold one:
m₁ c₁ (T₁ − T_f) = m₂ c₂ (T_f − T₂)
T_f = (m₁c₁T₁ + m₂c₂T₂ + C_cup·T₂) / (m₁c₁ + m₂c₂ + C_cup)
c is specific heat capacity (J/(g·K)), the energy to warm 1 g by 1 K. Water's c of 4.18 is unusually large, which is why a lot of hot metal barely warms a little water. The cup itself absorbs some heat; its heat capacity C_cup (J/K) is included.
The approach to equilibrium is modelled as Newtonian heat exchange between the block and the water, at a rate proportional to their temperature difference. The heat leak option lets the whole calorimeter slowly lose heat to a 20 °C room, as real coffee-cup calorimeters do.
No phase changes (temperatures stay between 0 and 100 °C for the water), well-stirred water, and constant specific heats. Values are typical textbook data.
A 50 g metal sample at 100 °C is dropped into 100 g of water at 20 °C, and the mix reaches 24.0 °C (ignore the cup). What is the metal's specific heat, and which metal might it be?
Heat gained by water: 100 × 4.18 × 4.0 = 1672 J. So c = 1672 / (50 × 76.0) ≈ 0.44 J/(g·K), close to iron (0.45). Set a custom metal with c = 0.44 to confirm.