Heat Capacity and Specific Heat
Heat capacity C = Q/ΔT (J/K). Specific heat c = C/m (J/(kg·K)). Molar heat capacity C_m = C/n (J/(mol·K)). For ideal gases: Cp − Cv = R; γ = Cp/Cv.
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Water c ≈ 4186 J/(kg·K); one of the highest; stabilizes climate Monatomic gas: γ = 5/3; diatomic: γ = 7/5; polyatomic: γ < 7/5 Cp > Cv always; Cp − Cv = R for ideal gases (Mayer relation) Dulong-Petit: molar heat capacity ≈ 3R for many solids at high T
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Why: Heat capacity determines temperature change for given heat input. Essential for thermal design, calorimetry, HVAC, and understanding gas behavior (γ for adiabatic processes).
How: Enter mass (or moles), temperature change, and heat (or select material). The calculator computes C, c, C_m, Cp, Cv, and γ.
Run the calculator when you are ready.
💧 Water Heating
Heating 1 kg of water from 20°C to 80°C using 251 kJ of energy
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🔩 Metal Cooling
Aluminum block (2 kg) cooling from 200°C to 25°C, releasing heat
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💨 Gas Compression
Compressing 0.5 kg of air at constant pressure, temperature rise from 20°C to 100°C
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🍲 Food Processing
Heating 0.5 kg of water-based food from 4°C to 100°C for cooking
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🔋 Battery Thermal Management
Lithium battery (0.1 kg) heating from 25°C to 60°C during charging
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Input Parameters
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For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Water has one of the highest specific heats (4186 J/(kg·K)); oceans moderate climate.
— NIST
Ideal gas: Cp − Cv = R = 8.314 J/(mol·K); Mayer relation.
— Thermodynamics
γ = 1.4 for air (diatomic); used in adiabatic process calculations.
— CRC
Dulong-Petit: C_m ≈ 25 J/(mol·K) for many solids at room temperature.
— Solid State
What is Heat Capacity?
Heat capacity (C) is a measure of how much heat energy is required to raise the temperature of a substance by one degree. It is an extensive property, meaning it depends on the amount of matter present.
Where Q is the heat energy transferred and ΔT is the temperature change. Heat capacity tells us how much energy a specific object can store or release when its temperature changes.
Specific Heat Capacity vs Heat Capacity
Heat Capacity (C)
Extensive property - depends on mass. Units: J/K
Example: A cup of water has different heat capacity than a bucket of water.
Specific Heat (c)
Intensive property - independent of mass. Units: J/(kg·K)
Example: Water always has specific heat of 4184 J/(kg·K), regardless of amount.
Cp vs Cv - Constant Pressure vs Constant Volume
Cp (Constant Pressure)
Heat capacity when pressure is held constant. Includes work done by expansion.
For ideal gases: Cp = Cv + R, where R is the gas constant.
Cv (Constant Volume)
Heat capacity when volume is held constant. No work is done by expansion.
For ideal gases: Cv represents only internal energy changes.
Gamma Ratio (γ)
For monatomic gases: γ ≈ 1.67
For diatomic gases: γ ≈ 1.40
For polyatomic gases: γ ≈ 1.33
For solids and liquids: γ ≈ 1.00 (Cp ≈ Cv)
Applications of Heat Capacity
Thermal Energy Storage
Materials with high heat capacity (like water) are excellent for storing thermal energy. Used in solar thermal systems and building thermal mass.
Climate Control
HVAC systems use heat capacity calculations to determine heating and cooling loads. Water's high heat capacity makes it ideal for heat transfer.
Food Processing
Cooking and food preservation rely on heat capacity to determine cooking times and energy requirements. Water-based foods heat more slowly due to high heat capacity.
Material Science
Understanding heat capacity helps in material selection for thermal management, insulation design, and thermal stress analysis in engineering applications.
❓ Frequently Asked Questions
What is the difference between heat capacity and specific heat capacity?
Heat capacity (C) is an extensive property that depends on the amount of matter - it's the total amount of heat needed to raise the temperature of an object by 1°C. Specific heat capacity (c) is an intensive property - it's the heat capacity per unit mass. Water has a specific heat of 4184 J/(kg·K) regardless of whether you have 1 gram or 1 kilogram.
Why does water have such a high specific heat capacity?
Water's high specific heat (4184 J/(kg·K)) comes from hydrogen bonding. When water is heated, energy first breaks hydrogen bonds between molecules before increasing molecular kinetic energy. This requires more energy per degree of temperature change, making water excellent for thermal regulation in biological systems and climate.
What is the difference between Cp and Cv?
Cp (heat capacity at constant pressure) includes energy for expansion work, while Cv (heat capacity at constant volume) includes only internal energy changes. For ideal gases, Cp = Cv + R, where R is the gas constant. For solids and liquids, Cp ≈ Cv since volume changes are minimal.
What does the gamma ratio (γ = Cp/Cv) tell us?
The gamma ratio indicates the type of gas: monatomic gases (He, Ar) have γ ≈ 1.67, diatomic gases (N₂, O₂) have γ ≈ 1.40, and polyatomic gases have γ ≈ 1.33. For solids and liquids, γ ≈ 1.0 since Cp ≈ Cv. The gamma ratio is crucial in adiabatic processes and sound speed calculations.
How does heat capacity vary with temperature?
Heat capacity generally increases with temperature as more vibrational and rotational modes become active. For example, water's specific heat increases from 4217 J/(kg·K) at 0°C to 4220 J/(kg·K) at 100°C. At very low temperatures, quantum effects can cause dramatic variations.
Why do metals have lower specific heat capacities than water?
Metals have lower specific heat (typically 100-900 J/(kg·K)) because their atoms are closely packed and can only store energy through atomic vibrations. Water molecules can store energy in multiple ways: translational, rotational, and vibrational motion, plus hydrogen bond breaking, resulting in much higher heat capacity.
How is molar heat capacity different from specific heat capacity?
Molar heat capacity (Cm) is heat capacity per mole of substance, measured in J/(mol·K). Specific heat capacity (c) is per unit mass, measured in J/(kg·K). They're related by Cm = c × M, where M is molar mass. Molar heat capacity is useful for comparing substances regardless of density.
📚 Official Data Sources
⚠️ Disclaimer
This calculator is for educational and scientific purposes. Heat capacity values assume standard conditions and may vary with temperature, pressure, and material purity. Actual values depend on phase, temperature range, and material composition. For critical applications in engineering, chemistry, or materials science, consult authoritative databases (NIST, IUPAC) and perform experimental verification when necessary. Material properties are approximate and may differ from manufacturer specifications.
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