Specific Heat by Method of Mixtures
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flagWhat you'll discover
- arrow_forwardState the principle of calorimetry (heat lost = heat gained)
- arrow_forwardCarry out the method of mixtures with correct readings θ₁, θ₂, θ
- arrow_forwardInclude the calorimeter’s water equivalent in the calculation
- arrow_forwardExplain how heat loss to the room biases the result and how to reduce it
The principle of calorimetry
When a hot solid meets cold water in an insulated vessel, heat flows until both reach a common temperature θ. If no heat escapes, heat lost by the solid equals heat gained by the water AND the calorimeter: mₛcₛ(θ₂ − θ) = (m_w c_w + m_c c_c)(θ − θ₁).
Everything except cₛ is measurable — masses on a balance, temperatures on a thermometer — so the solid’s specific heat follows from one equation. Water’s huge specific heat (4186 J/kg·K, about ten times copper’s) is why a small metal block barely warms the water by a few degrees.
Procedure, step by step
Weigh the dry copper calorimeter (m_c), add water and weigh again (giving m_w), and record the initial water temperature θ₁. Meanwhile heat the weighed solid in boiling water or a steam heater for ten minutes so it is uniformly at θ₂ ≈ 100 °C (check with a thermometer in the heater).
Transfer the solid QUICKLY — every second in the air sheds heat — and stir gently. The thermometer rises, peaks, then begins a slow fall as the room steals heat. The mixture temperature θ is the PEAK reading. Then compute cₛ = (m_w c_w + m_c c_c)(θ − θ₁) / mₛ(θ₂ − θ) and compare with standard values (copper 385, iron 450, aluminium 900 J/kg·K) to identify your metal.
Heat loss: the experiment’s great enemy
Real calorimeters leak heat by conduction, convection, radiation and evaporation, so your θ is always a little low and the computed cₛ comes out wrong. Defences: polish the calorimeter (shiny surfaces radiate less), sit it inside a padded wooden box, use a lid, start with water slightly BELOW room temperature so it first gains heat from the room and then loses — the two leaks partly cancel (a trick known as Rumford’s correction).
Other errors: water splashing during the drop, solid touching the calorimeter wall, thermometer not stirred to the true mixture temperature, and droplets of boiling water carried over with the solid. Toggle "heat loss" in the simulation and watch the computed value drift — that is precisely the systematic error your report must discuss.