Heat Capacity Calculator
Calculate heat energy, mass, specific heat, or temperature change using thermodynamic principles.
Temperature Change
Heat energy causes particles to move faster, raising the temperature.
The Physics of Thermal Energy
Understanding how substances store and transfer heat is fundamental to fields ranging from meteorology to culinary arts. This guide explores the relationship between mass, temperature, and material properties.
The Equation
The fundamental equation of calorimetry relates heat energy ($q$) to the properties of the object.
What does this mean?
Think of Specific Heat ($c$) as a "thermal price tag." It tells you how much energy you have to "pay" to raise the temperature of 1 gram of that material.
- HIGH CLike Water. Expensive to heat up. Stores a lot of energy.
- LOW CLike Metals. Cheap to heat up. Changes temp very quickly.
Common Specific Heat Values
| Substance | Phase | Specific Heat ($c$) [J/g°C] | Molar Heat Capacity [$J/mol·K$] |
|---|---|---|---|
| Water (Liquid) | Liquid | 4.184 | 75.3 |
| Ice | Solid | 2.09 | 37.7 |
| Steam | Gas | 2.03 | 36.5 |
| Aluminum | Solid | 0.897 | 24.2 |
| Iron | Solid | 0.449 | 25.1 |
| Copper | Solid | 0.385 | 24.4 |
| Gold | Solid | 0.129 | 25.4 |
Notice how most metals have a Molar Heat Capacity around 25 J/mol·K? This is known as the Law of Dulong and Petit.
Climate Regulation
Because water has such a high specific heat, oceans act as massive "heat sinks." They absorb solar energy during the day without getting too hot, and release it slowly at night. This is why coastal cities have milder climates than inland deserts.
Cooking Physics
Aluminum is used for pans because it heats up quickly (low specific heat) and conducts that heat to your food. However, cast iron (also low specific heat but higher mass) holds onto heat longer due to its sheer bulk heat capacity.
Industrial Coolants
Water is the coolant of choice for nuclear reactors and car engines not just because it's cheap, but because it can carry away massive amounts of heat ($q$) for every degree of temperature rise, keeping systems stable.
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Frequently Asked Questions
What is the difference between Heat Capacity and Specific Heat Capacity?
Heat Capacity (C) is an extensive property, meaning it depends on the amount of matter (e.g., a bathtub of water has a higher heat capacity than a cup). Specific Heat Capacity (c) is an intensive property, intrinsic to the material itself, defined per unit mass (usually 1 gram).
Why is the specific heat of water so high?
Water has a specific heat of 4.184 J/g°C, which is exceptionally high. This is due to hydrogen bonding. Heat energy must first break these strong intermolecular bonds before it can increase the kinetic energy (temperature) of the water molecules. This property makes water an excellent coolant and climate regulator.
How do I convert between Joules and Calories?
1 calorie (cal) is defined as the energy needed to raise 1g of water by 1°C. Therefore, 1 cal = 4.184 Joules. Be careful not to confuse 'cal' with dietary 'Calories' (kcal), which are 1000 calories.
What is Molar Heat Capacity?
Molar heat capacity ($C_m$) is the heat capacity per mole of substance rather than per gram. The formula is q = nCmΔT. It is often used in chemistry because it relates more directly to atomic structure. For metals, the Law of Dulong and Petit suggests Cm ≈ 3R (approx 25 J/mol·K).
Does specific heat change with temperature?
Yes, slightly. The value 4.18 J/g°C for water is an average. At 100°C (steam) or 0°C (ice), the specific heat is different (≈ 2.0 J/g°C for both). However, for most general calculations, we assume it is constant over small temperature ranges.
Why do metals feel colder than wood at the same temperature?
This is due to thermal conductivity, not just specific heat. Metals conduct heat away from your hand rapidly, making them feel cold. However, their low specifics heat also means they warm up quickly once they start absorbing energy.
How is specific heat used in calorimetry?
In a calorimeter, a hot object is placed in water. The heat lost by the object equals the heat gained by the water (-qobject = qwater). By measuring the water's temp rise, we can calculate the object's specific heat and mass ratios.
What are Cv and Cp in gases?
For gases, it matters how you heat them. Cv is specific heat at constant volume, and Cp is at constant pressure. Cp is always higher than Cv because when a gas expands (constant pressure), it does work, calculating extra energy.
Can ΔT be negative?
Yes. If the final temperature is lower than the initial temperature, ΔT is negative. This results in a negative q, which simply means heat energy was released (Exothermic process) rather than absorbed.
What is thermal inertia?
Thermal inertia generally refers to the combination of specific heat and thermal conductivity. High thermal inertia materials (like adobe or concrete) take a long time to heat up and cool down, which is why they are used in buildings to stabilize indoor temperatures.
Can I simple add temperatures when mixing liquids?
No, you cannot just average the temperatures unless the masses and specific heats are identical. You must use the principle of energy conservation: Heat Lost by Hot Water = Heat Gained by Cold Water.
What unit is c usually measured in?
The standard SI unit is J/kg·K, but in chemistry, we often use J/g·°C. Because the size of a Kelvin degree is the same as a Celsius degree, the numerical value for specific heat often remains easy to convert (just a factor of 1000 for kg vs g).
Does the formula work for melting ice?
No. The formula q=mcΔT is only for changing temperature within a phase. To calculate energy for melting (phase change), you must use q = mΔHfusion (Latent Heat), where there is no temperature change.
What is the Law of Dulong and Petit?
It is an empirical rule stating that the molar heat capacity of solid elements (especially metals) is approximately constant: roughly $3R$ or about 25 J/mol·K. This helps scientists estimate the atomic mass of unknown metals.
Why does sand get hotter than water at the beach?
Sand has a much lower specific heat (approx 0.8 J/g°C) than water (4.18 J/g°C). For the same amount of solar energy, the sand's temperature rises almost 5 times more than the water's.