Specific heat capacity

[1] In thermodynamics, a substance's specific heat capacity/specific heat/massic heat capacity (symbol c) is the amount of heat to add to a unit of the substance's mass to increase it by 1 temperature unit. More formally, it's the heat capacity of the substance's sample divided by its mass. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1.

E.g., the heat needed to raise the temperature of 1 kg of water by 1 K is 4184 J, so the specific heat water capacity is 4184 J⋅kg−1⋅K−1.

The specific heat capacity is defined as: c ≡ Q/(m*ΔT).

[1] Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about 4184 J⋅kg−1⋅K−1 at 20 °C, but that of ice, just below 0 °C, is only 2093 J⋅kg−1⋅K−1. The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 J⋅kg−1⋅K−1, and 14300 J⋅kg−1⋅K−1, respectively.[4] While the substance is undergoing a phase transition, such as melting or boiling, its specific heat capacity is technically undefined, because the heat goes into changing its state rather than raising its temperature.

[1] The specific heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (specific heat capacity at constant pressure) than when it is heated in a closed vessel that prevents expansion (specific heat capacity

at constant volume). These two values are usually denoted by cP and cV, respectively; their quotient γ = cP/cV is the heat capacity ratio

[1] The term specific heat may also refer to the ratio between a substance's specific heat capacities at a given temperature and of a reference substance at a reference temperature, like water at 15 °C; much in the fashion of specific gravity. Specific heat capacity is also related to other intensive measures of heat capacity with other denominators. If the amount of substance is measured as a number of moles, one gets the molar heat capacity instead, whose SI unit is joule per kelvin per mole, J⋅mol−1⋅K−1. If the amount is taken to be the volume of the sample (as is sometimes done in engineering), one gets the volumetric heat capacity, whose SI unit is joule per kelvin per cubic meter, J⋅m−3⋅K−1.

Specific heat formula

The specific heat formula allows to calculate the needed energy to heat a certain water mass.

Q = m*c*ΔT,

Q = energy (in J)
m = fluid volume/mass (in kg or lb)
c = thermal capacity (in J/(kg⋅°C) or BTU/(lb⋅°F)))
- for water: 4 190 J/(kg⋅°C)
ΔT = temperature difference (difference of initial to final temperature)

Proof and derivation by relationships A way to derive the formula is by rearrenging the energy over power formula t = Q/P for Q: Q = P*t.

If the amount of water doubles, it'd take twice as much as heat energy to reach the same temperature. Thus heat energy is directly proportional to mass: Q ∝ m.

Raising the temperature twice would also take twice as much energy. Thus heat energy is also directly proportional to tempreature difference: Q ∝ ΔT.

Combining the 2 equations results in a joint proportionality:

Q ∝ m*ΔT.

Introducing the specific heat capacity constant (c) turns the this proportionality into the formula: Q = m*c*ΔT.

Relationship of the energy over power formula and the specific heat formula The energy over power formula Q = P*t can also be turned into Q = m*c*ΔT, hence P*t = m*c*ΔT.

Heat refers to thermal energy when it moving into an object. How much thermal energy an object must absorb to change its temperature depends on its mass (m), its material properties (c), and how much hotter it gets (ΔT).

heat absorbed = m*c*ΔT

Energy over power formula

t = Q/P,

P = power (in W or J/s)
t = time (in sec)

References

[1] Wikipedia
[2]
[3]

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Specific heat capacity

Specific heat formula

Energy over power formula

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