# Specific heat capacity: formulas, applications, examples and frequently asked questions (2023)

Specific heat capacity is a physical property of matter. Specific heat capacity is defined as the amount of thermal energy required to raise the temperature of a substance per unit mass. It is also an example of extensive ownership. Because it is directly related to the size of the system under study. Hence, it is the amount of heat absorbed per unit mass of the substance when its temperature is increased. The units of specific heat are J/(kg K) or J/(kg °C). Let's learn more about specific heat capacity in this article!

## What is heat capacity?

The amount of thermal energy required to raise the temperature of a given amount of matter by one degree Celsius is calledheat capacity. The heat capacity of a given substance varies with its size or quantity, making it an extensive property.

Heat capacity is a measure of the total internal energy of a system. This includes the total kinetic energy of the system and the potential energy of the molecules. It has been shown that the internal energy of a system can be changed by adding or working on heat energy. It is shown that the internal energy of a system increases with increasing temperature. This increase in internal energy is affected by temperature differences, the amount of substance present, and so on.

Mathematically, the heat capacity results from:

Q = C∆T

• where Q is the amount of thermal energy required to cause a temperature change of ΔT and C is the heat capacity of the system under consideration.
• The unit of heat capacity isJoule pro Kelvin (J/K)ÖJoule per Degree Celsius (J/°C).

## specific heat capacity

The amount of heat energy required to raise the temperature of a substance per unit mass is called heat energyspecific heat capacity. The specific heat of a substance is a physical property. It is also an example of extensive property since its value is proportional to the size of the system under consideration. Specific heat capacity is generally a measure of how much energy is required to change the temperature of a system. However, it is important to understand that the energy contribution must come from heating. When working on the system, the temperature rises; However, attempting to calculate temperature rise via heat capacity and work done is inaccurate.

Another thing to consider is the limit to which the system is maintained. Since the latter acts on its surroundings as it expands, the specific heat capacity of a system maintained at constant volume differs from that of a system maintained at constant pressure. These discrepancies are often overlooked when working with solids, but are critical when working with gases.

## Specific heat capacity formula

The specific heat of a solid or liquid is the amount of heat required to raise the temperature of a unit mass of the solid by 1 °C. It is represented by the symbol C.

If ΔQ is the amount of heat required to raise the temperature of mass m to ΔT, then the formula for specific heat is:

C = ΔQ ⁄ Metro ΔT

Ö

ΔQ = Metro c ΔT

### SI unit of specific heat capacity

• It is the amount of heat required to raise the temperature of 1 kg of liquid or solid by 1 K in SI units.
• Its SI unit is always J kg.-1k-1.
• And your CGS unit is always Cal g-1C-1.
• The formula for measuring the specific heat capacity is [M0UE2T-2k-1].

## molar specific heat capacity

The molar specific heat of a solid or liquid is the amount of heat required to raise the temperature of one mole of a solid or liquid by one degree Celsius or one degree Kelvin.

It is marked with the letter C. Its unit is J mol-1k-1. To raise the temperature of μ mol solid by ΔT equals an amount of heatΔQ = μCTit would be necessary

The amount of heat required to raise 1 g of a molecule of a substance by one degree Celsius is called the molar specific heat of the substance, abbreviated C. The specific heat of water is assumed to be 1. This happens because water is used to define the unit of heat (calories).

## specific heat of water

The specific heat of water at normal pressure and temperature is about 4.2 J ⁄ g °C or 1 cal ⁄ g °C. This means that 1 gram of water requires 4.2 joules of energy to heat up 1 degree Celsius. That number is really high. At normal temperatures, water vapor also has a higher specific heat capacity than many other materials. The specific heat capacity of steam at normal pressure and temperature is about 1.9 J ⁄ g °C.

The temperature of water decreases when it gives off heat and increases when it absorbs heat, just like other liquids. But the temperature of liquid water either falls or rises more slowly than many other liquids. We can conclude that water absorbs heat without an immediate rise in temperature. It also keeps its temperature much longer than many other substances.

We use this property of water in the human body to keep it at a stable temperature. There would be many more instances of overheating and overheating if the water had a lower specific calorific value.

## Specific heat at constant pressure or volume

• When a solid is heated within a limited range of temperatures, its pressure remains constant.constant pressure, is calledSpecific heat, abbreviated asCPAG.
• When a solid is heated over a small range of temperatures, its volume remains constant.in constant volume, is calledSpecific heat, abbreviated asCv.

The way the gas is heated affects the behavior of the gas, the change in volume and pressure with temperature, and the amount of heat required to raise the temperature of 1 g of gas by 1 °C. We can heat the gas with different values ​​of P and V.

As a result, the value of the specific heat is unlimited. If we don't provide a constant amount of heat, the specific heat of the gas will change. As a result, we need a constant specific heat volume or pressure.

For an ideal gas,

CPAG- Cv= Nord R

Wovis the heat capacity at constant volume, CPAGthe heat capacity at constant pressure, R the molar constant of gases and n the amount of substance.

The value of the gas constant, R = 8.3145 J mol-1k-1

Heat capacity classification: CPAG⁄Cv

The adiabatic index is also known as the heat capacity ratio or specific heat capacity ratio (CPAG:Cv) in thermodynamics. The ratio of heat capacity at constant pressure (CPAG) for the heat capacity at constant volume (Cv) is defined as theheat capacity rate.

The isentropic expansion factor, commonly known as the heat capacity ratio, is denoted by γ for an ideal (gamma) gas. As a result, the specific heat ratio γ is equal to the ratio of CPAGfor Cv, so γ = CPAG⁄Cv.

## Why is it C?PAGBigger than Cv?

The specific heats of an ideal gas are represented by CPAGmi cv. This is the amount of heat required to raise the temperature of a unit mass by 1 °C. According to the first law of thermodynamics,

ΔQ = ΔU + ΔW

where ΔQ is the amount of heat added to the system, ΔU is the change in internal energy and ΔW is the work done.

At constant pressure, heat is absorbed to increase internal energy and do no work on the system. On the other hand, heat is only absorbed to increase internal energy at constant volume, and not to do work on the system. As a result, the specific heat at constant pressure is higher than at constant volume, i. H. Cp > Cv.

## Specific heat used

• Insulators use materials with a high specific heat capacity. Let's take wood for example. Wooden houses are best suited for areas with high or low temperatures.
• Pool water used to be cold due to the high specific heat of the water compared to the outside temperature.
• Cookware is made of a special low-temperature material. You can warm up your butt right away. This is due to the floors made of polished aluminum or copper. To keep our hands warm and protected, the handles of these utensils are made of special high-temperature material.

## Working examples of specific heat capacity

Example 1: Calculate the heat required to lift 0.5 kg of sand 30° C to 90°C? (Specific heat of the arena = 830 J ⁄ Kg °C)

Responder:

Given:

Sand mass, m = 0.5 kg

Temperature difference, ΔT = 90°C - 30°C = 60°C

Specific heat of arena, C = 830 J ⁄ Kg °C

The formula for specific heat capacity is:

C = ΔQ ⁄ Metro ΔT

Rewrite the formula for Q.

Q = U-Bahn C ΔT

= 0,5 kg × 830 J ⁄ kg °C × 60 °C

= 24900 J.

Therefore, the heat is required to increase the temperature of the sand24900J.

Example 2: Determine the temperature difference when 40 kg of water absorbs 400 KJ of heat.

Solution:

Given:

Mass of water, m = 40 kg

heat transfer, Q = 400 KJ,

Specific heat of water, c = 4.2 × 103J ⁄ kg °C

The formula for specific heat capacity is:

c = ΔQ ⁄ Metro ΔT

Rewrite the formula for ΔT.

ΔT = ΔQ ⁄ make Metro

= (400 × 103) ⁄ (4,2 × 103× 40) °C

= 2,38 °C

Question 1: What is the advantage of the heat capacity of water?

Responder:

Since water has a large heat capacity, increasing the temperature by one degree requires more energy. The sun gives off a relatively constant amount of energy, causing sand to heat up faster and water slower.

Question 2: What is the difference between heat capacity and specific heat capacity?

Solution:

Specific heat capacity is the heat required to raise the temperature of a substance by 1 degree Celsius. Likewise, heat capacity is the ratio between the energy added to a substance and the corresponding increase in its temperature.

Question 3: What is the ratio of the heat capacity?

Responder:

It is the relationship of two specific Heizkapazitäten, CPAGmi cvis given by: The heat capacity at constant pressure (CPAG)/ constant volume heat capacity (Cv).

The isentropic expansion factor, commonly known as the heat capacity ratio, is denoted by γ for an ideal (gamma) gas. As a result, the specific heat ratio γ is equal to the ratio of CPAGfor Cv, so γ = CPAG/Cv.

Question 4: How is specific heat capacity calculated?

Responder:

If ΔQ is the amount of heat required to raise the temperature of mass m to ΔT, then the formula for specific heat is:

C = ΔQ ⁄ Metro ΔT

Ö

ΔQ = Metro c ΔT

Question 5: What is the SI unit of specific heat capacity?

Responder:

It is the amount of heat required to raise the temperature of 1 kg of liquid or solid by 1 K in SI units. Its SI unit is always J kg.-1k-1. And your CGS unit is always Cal g-1C-1.

Question 6: What is specific heat capacity?

Responder:

The amount of thermal energy required to raise the temperature of a substance per unit mass is called its specific heat capacity.

Question 7: What is the specific heat capacity of ice, water and steam?

Responder:

The specific heat capacity of ice is 2108 kJ/kgK, water 4187 kJ/kgK and steam 1996 kJ/kgK.

Question 8: What is this?the specific heat capacity of air?

Responder:

The specific heat of air at constant pressure is 1.005 kJ/kg-K.

Question 9: How is the specific heat of gas calculated?

Responder:

The specific heat of the gas is calculated from CPAG⁄CvReason.

## related posts

• Thermal energy
• heat conduction
• latent heat

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