B.1 · IB Physics
Method of mixtures
Drop a hot metal block into water in an insulated cup and watch both temperatures converge. Change the metal, masses and starting temperatures to see how energy conservation fixes the final temperature.
mmcm(Tm − Tf) = mwcw(Tf − Tw)
Tf = (mmcmTm + mwcwTw) / (mmcm + mwcw)
cw = 4180 J kg⁻¹ K⁻¹
Status:
Metal temperature:
Water temperature:
Predicted Tf:
Energy lost by metal:
Energy gained by water:
Try this
- Keep 0.250 kg at 100 °C and 0.200 kg of water at 20 °C. Compare aluminium with lead: which warms the water more, and how does this follow from c?
- Double the water mass. Does the rise in water temperature halve? Check the change using the readouts.
- Watch the two energy bars during the animation: they stay equal at every instant. Then compare the two temperature changes — why is the metal’s ΔT usually much bigger?
Common error: each ΔT must be measured from that object’s own starting temperature to the shared final temperature, so write (Tm − Tf) for the metal and (Tf − Tw) for the water, never Tm − Tw.