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# Specific Heat Capacity

• Last Updated : 22 Sep, 2022

Specific heat capacity is a Physical Property of Matter. The specific heat capacity is defined as the amount of heat energy needed to increase the temperature of a substance per unit of mass. It is also an example of an extensive property. As it is directly related to the size of the system being studied. Hence, it is the quantity of heat absorbed per unit mass of the substance when its temperature is raised. The units of Specific Heat Capacity are J/(kg K) or J/(kg °C). Let’s learn more about the specific heat capacity in this article!

## What is the Heat Capacity?

The amount of heat energy necessary to increase the temperature of a given quantity of matter by one degree Celsius is known as Heat 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 a system’s total internal energy. This comprises the system’s overall kinetic energy as well as the potential energy of the molecules. It has been demonstrated that a system’s internal energy may be altered by either giving heat energy to it or doing work on it. The internal energy of a system is shown to grow as the temperature rises. This rise in internal energy is affected by temperature differences, the amount of substance present, and so on.

Mathematically, the heat capacity is given by:

Q = C ΔT

• where Q is the amount of heat energy necessary to cause a temperature change of ΔT and C is the heat capacity of the system under consideration.
• The unit of heat capacity is Joule per Kelvin (J/K) or Joule per degree Celsius (J/°C).

## Specific Heat Capacity

The quantity of heat energy required to increase the temperature of a substance per unit mass is referred to as its Specific Heat Capacity. The specific heat capacity of a substance is a physical characteristic.

It is also an example of an extensive property because its value is proportional to the size of the system under consideration. Specific heat capacity, in general, is a measure of how much energy it takes to change the temperature of a system. However, it is critical to understand that the energy intake must be through heating. If work is done on the system, the temperature will rise; however, attempting to compute the temperature rise using the heat capacity and the quantity of work done on it is inaccurate.

Another thing to consider is the limitation that the system is held to. Because the latter does work on its surroundings as it expands, the specific heat capacity of a system kept at constant volume differs from that of a system held at constant pressure. Such discrepancies are typically overlooked when dealing with solids, but they are critical when working with gases.

## Specific Heat Capacity Formula

A solid’s or liquid’s specific heat is the amount of heat required to increase the temperature of the unit mass of the solid by 1° C. It is represented by the symbol C.

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

C = ΔQ ⁄ m ΔT

or

ΔQ = m c ΔT

### SI Unit of Specific Heat Capacity

• It is the amount of heat required to increase the temperature of 1 kg of liquid or solid by 1 K in SI units.
• Its SI unit is always J kg-1 K-1.
• And its CGS unit is always Cal g-1 C-1.
• The Dimensional Formula of Specific Heat Capacity is [M0 L2 T-2 K-1].

## Molar Specific Heat Capacity

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

It is denoted by the letter C. Its unit is J mol-1 K-1. To raise the temperature of μ moles of solid by ΔT, a quantity of heat equal to ΔQ = μ C T would be required.

The quantity of heat required to increase the temperature of 1 gm molecule of a substance by one-degree centigrade is known as the molar specific heat capacity of the substance, abbreviated as C. Water’s specific heat is assumed to be 1. This is because we used water to define the unit of heat (calories).

## Specific Heat of Water

The specific heat capacity of water at normal pressure and temperature is approximately 4.2 J ⁄ g °C or 1 Cal ⁄ g °C. This means that 1 gm of water requires 4.2 joules of energy to raise 1 degree Celsius. This number is actually pretty high. Even water vapor has a higher specific heat capacity than many other materials at normal temperatures. Water vapor’s specific heat capacity at normal pressure and temperature is approximately 1.9 J ⁄ g °C.

Water’s temperature falls as it releases heat and rises as it absorbs heat, as it is with other liquids. But the liquid water temperature falls or rises slower than that of many other liquids. We may conclude that water absorbs heat without causing an instant temperature increase. It also keeps its temperature for a considerably longer period of time than many other substances.

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

## Specific Heat at Constant Pressure or Volume

• When a solid is heated over a limited temperature range, its pressure remains constant. At constant pressure, this is referred to as specific heat, abbreviated as CP.
• When a solid is heated over a short temperature range, its volume remains constant. At constant volume, this is referred to as specific heat, abbreviated as CV.

The way gas is heated affects the behavior of the gas, the volume and pressure change in temperature, and the amount of heat necessary to increase the temperature of 1gm of gas by 1° C. We can heat the gas with a variety of P and V values.

As a result, the specific heat value is limitless. If we don’t deliver a steady quantity of heat, the gas’s specific heat will change. As a result, we will need a constant pressure or volume of specific heat.

For an ideal gas,

CP – CV = n R

where, CV is heat capacity at constant volume, CP is heat capacity at constant pressure, R is the molar gas constant, and and n is amount of substance.

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

Heat Capacity Ratio: CP ⁄ CV

The adiabatic index is also known as the heat capacity ratio or ratio of specific heat capacities (CP:CV) in thermodynamics. The ratio of heat capacity at constant pressure (CP) to heat capacity at constant volume (CV) is defined as the heat capacity ratio.

The isentropic expansion factor, commonly known as heat capacity ratio, is indicated by γ for an ideal gas (gamma). As a result, specific heat ratio, γ is equal to ratio of CP to CV, i.e. γ = CP ⁄ CV.

## Why is CP Greater than CV?

The specific heats of an ideal gas are represented by CP and CV. This is the amount of heat required to raise the temperature of unit mass by 1° C. By the first law of thermodynamics,

ΔQ = ΔU + ΔW

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

At constant pressure, heat is absorbed to raise internal energy and do any work on the system. On the other side, heat is absorbed just to raise internal energy at constant volume, not to do any work on the system. As a result, the specific heat under constant pressure is greater than that at constant volume, i.e. Cp > Cv.

## Uses of Specific Heat Capacity

• Insulators make use of materials with a high specific heat capacity. Take, for instance, wood. Houses built of wood are better suitable for areas with high or low temperatures.
• Swimming pool water used to be cold in comparison to the temperature outdoors due to the high specific heat of the water.
• Cooking utensils are made of a low-specific-heat material. You can immediately heat their bottoms. This is due to their polished aluminum or copper bottoms. To maintain the heat and safeguard our hands, the handles of these utensils are made of high-specific heat material.

## Solved Examples on Specific Heat Capacity

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

Answer:

Given:

Mass of sand, m = 0.5 Kg

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

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

The formula for specific heat capacity is given as:

C = ΔQ ⁄ m ΔT

Rearrange the formula in terms of Q.

Q = m C ΔT

= 0.5 Kg × 830 J ⁄ Kg °C×  60° C

= 24900 J.

Hence, the required heat to raise the sand temperature is 24900 J.

Example 2: Determine the temperature difference if 40 Kg of water absorbs 400 K J of heat.

Solution:

Given:

Mass of water, m = 40 Kg

Heat transfer, Q = 400 KJ,

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

The formula for specific heat capacity is given as:

c = ΔQ ⁄ m ΔT

Rearrange the formula in terms of ΔT.

ΔT = ΔQ ⁄ c m

= (400 × 103) ⁄ (4.2 × 103 × 40) °C

= 2.38 °C

Hence, the temperature difference is 2.38 °C.

## FAQs on Specific Heat Capacity

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

Answer:

Because water has a large heat capacity, a one-degree increase in temperature necessitates more energy. The sun emits a relatively consistent amount of energy, which causes sand to heat up faster and water to heat up slower.

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

Solution:

Specific heat capacity is the heat needed to raise a substance’s temperature by 1 degree Celsius. Similarly, heat capacity is the ratio between the energy provided to a substance and the corresponding increase in its temperature.

Question 3: What is the Heat Capacity Ratio?

Answer:

It is the ratio of two specific heat capacities, CP and CV is given by: The Heat Capacity at Constant Pressure (CP)/ Heat capacity at Constant Volume (CV).

The isentropic expansion factor, commonly known as the heat capacity ratio, is indicated by γ for an ideal gas (gamma). As a result, the specific heat ratio, γ is equal to the ratio of CP to CV, i.e. γ = CP / CV.

Question 4: How do you calculate the Specific Heat Capacity?

Answer:

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

C = ΔQ ⁄ m ΔT

or

ΔQ = m c ΔT

Question 5: What is the SI unit of Specific Heat Capacity?

Answer:

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

Question 6: What is Specific Heat Capacity?

Answer:

The quantity of heat energy required to increase the temperature of a substance per unit mass is referred to as its Specific Heat Capacity.

Question 7: What is the Specific Heat Capacity of Ice, Water, and Steam?

Answer:

The Specific Heat Capacity of Ice is 2.108 kJ/kgK, Water is 4.187 kJ/kgK, and Steam is 1.996 kJ/kgK.

Question 8: What is the Specific Heat Capacity of Air?

Answer:

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

Question 9: How Specific Heat of Gas is calculated?

Answer:

The Specific Heat of Gas is calculated by CP ⁄ CV ratio.

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