Thermal Equilibrium Calculator

The standard mixing formula assumes no heat exchange with the surroundings. Real cups and calorimeters lose some heat to the air, so measured final temperatures may be slightly lower than the ideal prediction.

Yes. Each term in the numerator and denominator uses its own $mc$ product. Metal shot in water, for example, has much lower specific heat, so it has less influence on the final temperature than the same mass of water.

The equilibrium temperature always lies between the two initial values. It cannot exceed the hotter starting temperature or fall below the colder one unless external heat is added or removed.

Heat lost by the warmer sample equals heat gained by the cooler sample: $m_1 c_1 (T_1 - T_{eq}) = m_2 c_2 (T_{eq} - T_2)$. The calculator reports both values for verification.

This model assumes no melting, boiling, or freezing. If a substance crosses a phase boundary, latent heat must be included and the final temperature may stay at the phase-change point until the transition completes.