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Specific Heat Calculator

The specific heat equation Q = mcΔT relates heat energy transferred (in joules) to the mass of a substance, its specific heat capacity, and the temperature change. Given any three of these four values, the fourth can be calculated. Select which variable to solve for, enter the known values, and this calculator returns the result instantly.

Quick Answer

Heating 100 g of water (c = 4.186 J/g°C) by 25°C requires Q = 100 x 4.186 x 25 = 10,465 J of heat energy.

Common Examples

Input Result
m = 100 g, c = 4.186 J/g°C, deltaT = 25°C Q = 10,465.00 J
Q = 5,000 J, c = 0.897 J/g°C, deltaT = 50°C m = 111.48 g
Q = 8,000 J, m = 200 g, deltaT = 10°C c = 4.00 J/g°C
Q = 15,000 J, m = 500 g, c = 0.385 J/g°C deltaT = 77.92°C
m = 250 g, c = 2.44 J/g°C, deltaT = 40°C Q = 24,400.00 J

How It Works

The Formula

The specific heat equation (also called the calorimetry equation) describes the relationship between heat energy and temperature change:

Q = m x c x ΔT

Where:

  • Q = heat energy transferred, in joules (J)
  • m = mass of the substance, in grams (g)
  • c = specific heat capacity, in joules per gram per degree Celsius (J/g°C)
  • ΔT = change in temperature, in degrees Celsius (°C)

This equation can be rearranged to solve for any variable:

  • Heat energy: Q = m x c x ΔT
  • Mass: m = Q / (c x ΔT)
  • Specific heat: c = Q / (m x ΔT)
  • Temperature change: ΔT = Q / (m x c)

What Is Specific Heat Capacity?

Specific heat capacity (c) is a material property that describes how much energy is needed to raise one gram of a substance by one degree Celsius. A high specific heat means the substance absorbs more energy per degree of temperature change. Water has a notably high specific heat of 4.186 J/g°C, which is why it heats and cools slowly compared to metals.

Common Specific Heat Values (J/g°C):

  • Water: 4.186
  • Ethanol: 2.44
  • Ice (at 0°C): 2.09
  • Aluminum: 0.897
  • Iron: 0.449
  • Copper: 0.385
  • Gold: 0.129

Sign Conventions

A positive Q means the substance absorbs heat (endothermic process, temperature increases). A negative Q means the substance releases heat (exothermic process, temperature decreases). The ΔT value can be positive or negative accordingly.

Worked Example

To find the heat energy required to raise 100 g of water from 20°C to 45°C: ΔT = 45 - 20 = 25°C. Q = 100 x 4.186 x 25 = 10,465 J (or 10.465 kJ). To find the specific heat of an unknown metal, suppose 8,000 J raises 200 g by 10°C: c = 8,000 / (200 x 10) = 4.00 J/g°C. To find the temperature change when 15,000 J heats 500 g of copper (c = 0.385): ΔT = 15,000 / (500 x 0.385) = 77.92°C.

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Frequently Asked Questions

What is specific heat capacity?
Specific heat capacity is the amount of heat energy (in joules) required to raise one gram of a substance by one degree Celsius. It is an intrinsic property of a material. Substances with high specific heat capacity, like water (4.186 J/g C), resist temperature changes more than substances with low specific heat, like copper (0.385 J/g C).
Why does water have such a high specific heat?
Water molecules form extensive hydrogen bonds with neighboring molecules. Breaking and reforming these bonds requires significant energy, which means water absorbs a large amount of heat before its temperature rises noticeably. This property makes water an excellent coolant and is also why coastal climates tend to be more moderate than inland climates.
What units should I use?
This calculator uses grams (g) for mass, joules (J) for energy, and degrees Celsius for temperature. If your mass is in kilograms, multiply by 1,000 to convert to grams. If your energy is in calories, multiply by 4.184 to convert to joules (1 calorie = 4.184 J).
Can I use this formula for phase changes like melting or boiling?
No. The Q = mcΔT formula applies only to temperature changes within a single phase. During a phase change (melting, boiling, freezing, condensation), the temperature stays constant while energy is absorbed or released. Phase changes use a different formula: Q = mL, where L is the latent heat of the transition.
What is the difference between specific heat and heat capacity?
Specific heat capacity (c) is the energy per gram per degree for a material. Heat capacity (C) is the energy per degree for a specific object, calculated as C = m x c. Specific heat is a material property that does not depend on the amount of substance, while heat capacity depends on both the material and the mass.