Heat Transfer Calculator
Calculate heat transfer, specific heat capacity, mass, and temperature change using thermodynamic equations
Heat Energy (Q)
Mass (m)
Specific Heat (c)
Temp. Change (ΔT)
Step-by-Step Solution
Heat Flow Rate (Q/t)
Thermal Resistance (R)
Step-by-Step Solution
Heat Transfer Formulas
Heat transfer is the movement of thermal energy from one object or substance to another due to a temperature difference. There are three fundamental modes of heat transfer: conduction, convection, and radiation.
Calorimetry Equation
Q = m × c × ΔT
- Q = heat energy transferred (Joules)
- m = mass of the substance (kg)
- c = specific heat capacity (J/(kg·K))
- ΔT = change in temperature (K or °C)
Fourier's Law of Heat Conduction
Q/t = k × A × ΔT / d
- Q/t = rate of heat transfer (Watts)
- k = thermal conductivity (W/(m·K))
- A = cross-sectional area (m²)
- ΔT = temperature difference across the material (K or °C)
- d = thickness of the material (m)
Variables
- Q — Heat energy (J). 1 kJ = 1,000 J; 1 cal ≈ 4.184 J.
- m — Mass of the substance being heated or cooled (kg).
- c — Specific heat capacity, the energy required to raise 1 kg by 1 K. Water has one of the highest at 4,186 J/(kg·K).
- ΔT — Temperature change. A change of 1°C equals a change of 1 K.
- k — Thermal conductivity, a material property describing how well it conducts heat. Metals have high k values; insulators have low k values.
Common Specific Heat Capacities
| Material | c [J/(kg·K)] | Notes |
|---|---|---|
| Water (liquid) | 4,186 | Highest among common substances |
| Ice | 2,090 | At 0°C |
| Steam | 2,010 | At 100°C and 1 atm |
| Air | 1,005 | At constant pressure |
| Aluminum | 900 | Lightweight, good conductor |
| Sand | 840 | Explains hot beach sand |
| Ethanol | 790 | Common solvent |
| Glass | 710 | Borosilicate glass |
| Iron / Steel | 449 | Cast iron |
| Copper | 385 | Excellent thermal conductor |
| Lead | 235 | Dense metal |
| Gold | 129 | Low specific heat |
| Silver | 128 | Highest thermal conductivity of metals |
Modes of Heat Transfer
Conduction
Transfer of heat through direct molecular contact within a solid or between objects in contact.
- • Governed by Fourier's Law
- • Depends on thermal conductivity (k)
- • Metals are excellent conductors
- • Example: touching a hot pan
Convection
Transfer of heat through the bulk movement of fluids (liquids or gases).
- • Newton's Law of Cooling: Q/t = hAΔT
- • Natural or forced convection
- • Driven by buoyancy or external forces
- • Example: boiling water, wind chill
Radiation
Transfer of heat through electromagnetic waves without requiring a medium.
- • Stefan–Boltzmann Law: Q/t = εσAT⁴
- • No physical contact required
- • Depends on surface emissivity
- • Example: sunlight warming Earth
References
The formulas and material property data used in this calculator are based on established thermodynamics principles and peer-reviewed sources:
- Engineering ToolBox – Specific Heat Capacity of common Substances
- Engineering ToolBox – Thermal Conductivity of common Materials
- NIST – Fundamental Physical Constants
- OpenStax University Physics Vol. 2 – Heat Transfer, Specific Heat, and Calorimetry
- HyperPhysics – Heat Transfer
- Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2006). Fundamentals of Heat and Mass Transfer (6th ed.). John Wiley & Sons.
- Çengel, Y. A., & Boles, M. A. (2014). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill Education.
Related Calculators
Note: This calculator uses idealized thermodynamic equations and standard material properties at room temperature. Real-world results may vary due to factors such as temperature-dependent material properties, heat losses to the environment, phase changes, and non-uniform heat distribution.
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