Heat vs Temperature Simulator

What Is the Heat vs Temperature Simulator?

Same Heat, Two Different Temperatures

Pour the exact same amount of heat into two beakers of water and you might expect them to end up equally warm. They will not. When Beaker A mass is small and Beaker B mass is large, the identical energy lifts the little beaker far higher up the thermometer while the big one barely stirs. That gap is the whole lesson: heat and temperature are two separate ideas. Heat is the energy in joules you transfer; temperature (°C) is only how hot the water feels, set by the average kinetic energy of its particles.

The readout Q = m·c·ΔT ties them together. Rearranged, ΔT = Q/(m·c), so a bigger mass in the denominator means a smaller change in temperature for the same Q. Slide Temperature change up and watch Q climb, then split the same Q between unequal masses and compare. A large, cool tank can store far more thermal energy than a small, scalding cup, so a high reading never guarantees a lot of heat is present.

Adjust the Start temperature too and notice that energy always drains from the hotter body toward the cooler one until both settle at thermal equilibrium. Once you can predict each beaker's rise by eye, pin down real numbers with the specific heat calculator, then keep experimenting across the wider collection of physics simulations.

Where the ideal heat and temperature model breaks down

The simulator gives every joule to the water. A real beaker does not. Borosilicate glass has a specific heat around 750 J/(kg·°C), so a 250 g beaker warming through the same 30 °C absorbs 0.25 × 750 × 30 = 5,625 J before the water sees any of it. Against Beaker A's 251,160 J that is 2.2%, easy to ignore. Against Beaker B's 62,790 J it is 9% — the difference between a tidy result and one that will not close. The thermometer, the stirrer and the hotplate top all take their cut as well.

Nothing here takes time, either. Q = m·c·ΔT is a bookkeeping statement about the start and end states; it says nothing about the minutes in between, and during those minutes the beaker leaks. Warm water convects heat into the room and conducts it into the bench, and it does so faster the further above room temperature it climbs. That penalty grows with heating time, which is why the slow 5.0 kg beaker misses its predicted temperature by more than the quick 0.1 kg one.

Evaporation is the loss students miss, because it happens well below boiling. Every gram of water that leaves the surface carries roughly 2,260 J of latent heat away with it. Lose a single gram from Beaker B and you have removed 2.26 kJ — 3.6% of the 62.79 kJ the readout says you supplied — and trimmed the m in m·c·ΔT at the same time. Over a long heat in a wide beaker, several grams can go.

Two smaller idealisations round it out. The lab pins c at 4,186 J/(kg·°C) for every temperature, whereas real water's value drifts by about a percent across the liquid range — smaller than any loss above. And the sim is honest about the wall it hits: set Start to 50 °C and Change to 80 °C and it clamps the target to 100 °C, warning that further energy goes into the phase change. That wall is not a small one. Boiling 0.5 kg of water away takes about 1,130 kJ, eighteen times the 62.79 kJ that warmed it 30 °C in the first place.

Where this is actually used

An electric kettle is this equation with a plug on it. Set Beaker B to 0.5 kg, Start to 20 °C and Change to 80 °C — half a litre taken to boiling — and the readout gives 167,440 J. A 2,200 W kettle delivers 2,200 joules every second, so it needs 167,440/2,200 ≈ 76 seconds. That is a number you can check against your own kitchen clock, and whatever your kettle takes beyond 76 s is the losses described above.

Scale the same sum up and it becomes a household energy bill. A 150-litre hot-water cylinder heated from 15 °C to 60 °C stores 150 × 4,186 × 45 = 28.3 MJ, or 7.85 kWh. That is roughly seventeen times the most this lab can ask for in one go — 5.0 kg through 80 °C reads 1,674,400 J — and it is why the hot-water tank is one of the largest single loads in a house.

Water's specific heat is also the reason it, rather than air, carries heat around a building or an engine. Per cubic metre, water holds 4,186,000 J for each degree of rise; air, at about 1.2 kg per cubic metre, holds roughly 1,200 J — some 3,500 times less. A radiator circuit can therefore move a room's worth of heat through a 15 mm pipe, where a ducted air system needs a duct you could crawl through. The lab shows the same principle at its own scale: set Beaker A to 5.0 kg and Beaker B to 0.1 kg at a 30 °C change and the bars read 627.90 kJ against 12.56 kJ, exactly fifty to one.