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Two-Body Thermal Equilibrium Temperature — result sheet
Calculate the final equilibrium temperature and signed heat transfer for two bodies sharing heat in an isolated constant-specific-heat model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Tf = (m1 c1 T1 + m2 c2 T2) / (m1 c1 + m2 c2); signed heat transfer to body 1 is Q1 = m1 c1 (Tf - T1).
This calculator applies an isolated two-body calorimetry balance with constant specific heats. It returns the heat-capacity-weighted final temperature and heat transferred to body 1, where a positive Q1 means body 1 gains heat; phase changes, heat loss, container capacity, and time rates are outside the model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mass 1 — kg; Finite positive mass of body 1 in kilograms.; minimum 1.0E-6; maximum 1000000
- Specific heat 1 — J/(kg K); Finite positive constant specific heat of body 1.; minimum 1.0E-6; maximum 1000000
- Initial temperature 1 — K; Finite nonnegative initial absolute temperature of body 1.; minimum 0; maximum 1000000
- Mass 2 — kg; Finite positive mass of body 2 in kilograms.; minimum 1.0E-6; maximum 1000000
- Specific heat 2 — J/(kg K); Finite positive constant specific heat of body 2.; minimum 1.0E-6; maximum 1000000
- Initial temperature 2 — K; Finite nonnegative initial absolute temperature of body 2.; minimum 0; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Mass 1 | 1 |
| Specific heat 1 | 4186 |
| Initial temperature 1 | 293.15 |
| Mass 2 | 1 |
| Specific heat 2 | 4186 |
| Initial temperature 2 | 373.15 |
Equal water-like heat capacities reach 333.15 K; body 1 gains 167440 J in this isolated model.
Assumptions and limits
- Both masses and specific heats are finite positive SI quantities, and both initial temperatures are finite nonnegative absolute temperatures in kelvins.
- Each body has constant specific heat over the interval, remains in one phase, and reaches one common final equilibrium temperature.
- The two bodies form an isolated thermal system with no heat loss, no external work, and no unentered container or environmental heat capacity.
- Heat transfer to body 1 is signed as Q1 = m1 c1 (Tf - T1); a negative value means body 1 loses heat.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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