How this calculator works
The final temperature balances the energy gained and lost by two bodies plus any external heat. With constant specific heats it is a heat-capacity-weighted average. Optional phase mode represents one transition in the first body and a constant-specific-heat second body. If the total energy falls inside the latent-heat plateau, the final temperature equals the transition temperature and only part of the first body changes phase.
Formula
Without a transition: Tf = (m1 c1 T1 + m2 c2 T2 + Q_external)/(m1 c1 + m2 c2). With a transition: H1(Tf) + H2(Tf) = H1(T1) + H2(T2) + Q_external, including m1 L on the plateau.
Worked example
Two 1 kg bodies with c = 1000 J/(kg K), initially 300 and 400 K, reach 350 K and transfer 50000 J. If the 300 K body instead has mass 2 kg, the same hot body gives 330 K.
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Frequently asked questions
Does a simple average always work?
Only when the bodies have equal total heat capacities. Different masses or specific heats require a weighted average.
What if the first body starts at its transition?
Select its initial phase. Temperature alone cannot tell whether its latent energy has already been absorbed.
Does the model include the container?
No. Include its heat capacity in a body if it stays at that body's temperature, or use a more detailed calorimetry model.