2,000
2,000
J/°C
2
kJ/°C
10,000
J
10
kJ
5
°C
2,092
J/°C
2,000
2,000
J/°C
2
kJ/°C
10,000
J
10
kJ
5
°C
2,092
J/°C
The Heat Capacity Calculator determines the heat capacity (C) of a system or solves related thermal problems using the equation q = CΔT. Heat capacity is an extensive property that depends on both the substance and the amount present — it represents the total heat required to change the temperature of an entire object or system by one degree. Unlike specific heat (per gram), heat capacity applies to the whole sample. This calculator also converts between heat capacity and specific heat using C = mc. It is essential for calorimeter calibration, thermal system design, HVAC engineering, and understanding the thermal behavior of composite systems.
Heat capacity relates heat to temperature change for an entire system:
$$q = C \cdot \Delta T$$
where C is the heat capacity (J/°C), q is heat (J), and ΔT is temperature change (°C). Solving for each variable:
$$C = \frac{q}{\Delta T}, \quad q = C \cdot \Delta T, \quad \Delta T = \frac{q}{C}$$
Heat capacity can also be calculated from mass and specific heat:
$$C = m \cdot c$$
For composite systems (e.g., calorimeter + water):
$$C_{total} = m_1 c_1 + m_2 c_2 + ...$$
The molar heat capacity (Cm = C/n) is another useful quantity, with units of J/(mol·°C).
A higher heat capacity means the system can absorb more heat with less temperature change — it acts as a better thermal reservoir. The heat capacity of a calorimeter (including the bomb, water, and accessories) must be known for accurate calorimetry. The C = mc relationship lets you convert between the extensive (C) and intensive (c) forms. For thermal engineering, knowing the total heat capacity helps predict how quickly a system heats or cools.
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Results
C = 10000/4.75 = 2105.3 J/°C. This is the total heat capacity of the calorimeter system. Known heat input (e.g., from burning benzoic acid) and measured ΔT gives C.
Inputs
Results
C = 500 g × 4.184 J/(g·°C) = 2092 J/°C. This is the heat capacity of 500 g of water. To heat it by 5°C requires 2092 × 5 = 10,460 J.
Heat capacity (C) is the amount of heat energy required to raise the temperature of an entire object or system by 1 degree. It is an extensive property — it depends on the amount of material.
Specific heat (c) is per unit mass: J/(g·°C). Heat capacity (C) is for the whole sample: J/°C. They are related by C = mc. Specific heat is intensive (doesn't depend on amount), heat capacity is extensive.
Molar heat capacity (Cm) is the heat capacity per mole of substance: J/(mol·°C). For ideal monatomic gases, Cv,m = 3R/2 ≈ 12.5 J/(mol·K). For ideal diatomic gases, Cv,m = 5R/2 ≈ 20.8 J/(mol·K).
By burning a substance of known ΔH (like benzoic acid, ΔH = −26,454 J/g) and measuring the temperature rise. Ccal = q/ΔT. This calibration must be done before unknown samples are measured.
Heat capacity varies with temperature. It is approximately constant near room temperature but changes significantly near phase transitions and at very low temperatures (approaching zero at 0 K per the third law).
The specific heat of water is 4.184 J/(g·°C). For 1 kg of water, C = 4184 J/°C. For 1 mole (18.015 g), Cm = 75.4 J/(mol·°C).
In statistical mechanics, each degree of freedom contributes R/2 to the molar heat capacity. Monatomic gases have 3 translational DOF (Cv = 3R/2). Diatomic gases add 2 rotational DOF (Cv = 5R/2).
The Debye model explains how heat capacity of solids varies with temperature. At high T, it approaches the Dulong-Petit limit (3R per mole). At low T, it decreases as T³, reaching zero at absolute zero.
In normal thermodynamic systems, heat capacity is always positive. Negative heat capacity can occur in gravitational systems (like stars) where adding energy causes expansion and cooling — a purely astrophysical phenomenon.
Engineers use heat capacity to design heat exchangers, size heating/cooling systems, determine thermal response times, and calculate energy storage in thermal mass systems (like building materials).
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