Specific Heat Capacity is one of the fundamental physical properties of matter that describes the amount of heat energy required to increase the temperature of 1 kg of matter by 1o Celsius. the SI unit of Specific Head Capacity is J/(KgK), but other than this Specific Heat Capacity is also measured in cal/(gK) or J/(g°C). For any matter, specific heat capacity depends on its composition, density, and the physical state of the matter, as for the different states of water specific heat is different.
With this article, we will learn about the concept of Specific Heat Capacity and the other concepts in thermodynamics related to it.
Heat Capacity
The amount of heat energy required to increase the temperature of a given quantity of matter by 1°C, is known as the Heat Capacity of that matter. Heat Capacity is an extensive property of matter as it varies with the size and quantity of the matter.
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 and the amount of substance present in the system
Mathematically, the heat capacity is given by:
c = Q /ΔT
where,
- Q is the amount of heat energy necessary to cause a temperature change of ΔT
- c is the heat capacity of the system under consideration.
Unit of Heat Capacity
The SI unit of heat capacity is Joule per Kelvin (J/K) or Joule per degree Celsius (J/°C).
Specific Heat Capacity
Specific Heat Capacity is a physical characteristic of the system and is defined as the amount of energy required to increase the temperature of 1 unit substance by 1°C.
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 the formula for specific heat is:
C = ΔQ ⁄ m ΔT
ΔQ = m c ΔT
Unit of Specific Heat Capacity
As it is the amount of heat required to increase the temperature of 1 kg of matter by 1 K. Thus,
- SI unit of Specific Heat Capacity is always J kg-1 K-1.
- In the cgs system, the unit of Specific Heat Capacity, Cal/(g°C) or J/(g°C)
- Dimensional Formula of Specific Heat Capacity is [M0 L2 T-2 K-1]
Specific Heat Capacity of Various Substances
The specific Heat Capacity of various substances in their different states of matter is shown in the following table.
| Water |
Liquid
|
4.18
|
| Water |
Solid
|
2.06
|
| Water |
Gas
|
1.87
|
| Ammonia |
Gas
|
2.09
|
| Ethanol |
Liquid
|
2.44
|
| Aluminum |
Solid
|
0.897
|
| Carbon(Graphite) |
Solid
|
0.709
|
| Copper |
Solid
|
0.385
|
| Gold |
Solid
|
0.129
|
| Iron |
Solid
|
0.449
|
| Lead |
Solid
|
0.129
|
| Mercury |
Liquid
|
0.14
|
| Silver |
Solid
|
0.233
|
Molar Specific Heat
The molar specific heat of a matter is an amount of heat required to raise the temperature of one mole of substance by 1 °C or 1 °K.
Molar Specific Heat Capacity is denoted by the third alphabet of the English language “c”(lower case) and its unit is J/(mol K) or J/(mol °C). Mathematically Molar Specific Heat is given by the following formula:
c = Q/(n ΔT)
Q = ncΔT
where,
- Q is the amount of energy required to chagne temperature by ΔT
- n is the number of moles of the substance
- c is the specific heat of the system under considertation
Note: This formula tells us how much energy is required to raise the temperature of n moles of solid by ΔT.
Specific Heat of Water
Specific heat capacity of water at NTP(normal pressure and temperature) is approximately 4.2 J ⁄ (g°C) or 1 Cal ⁄(g°C) which implies that we need 4.2 joules of energy to raise the temperature of 1 gm of water by1 °C.
As water is not a conductor of heat, thus this number is actually pretty high compared to the other substances. 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). For the solid form of water i.e., ice, the specific heat capacity is 2.06 J ⁄ (g°C).
Water has a high specific heat capacity, which means that its temperature changes more slowly compared to other liquids when it absorbs or releases heat. This property allows water to absorb heat without causing an instant temperature increase and to retain its temperature for a longer period than many other substances. In the human body, we use this property of water to maintain a stable body temperature. A lower specific heat value of water would result in a higher risk of underheating and overheating in our bodies.
Specific Heat at Constant Pressure and Constant Volume
The specific heat at constant pressure and constant volume is discussed below in the article.
Specific Heat at Constant Pressure
The specific heat capacity at constant pressure (CP) is the amount of heat energy required to increase the temperature of a substance by one degree Celsius or Kelvin while keeping the pressure constant. CP includes the heat energy required to raise the temperature of the substance as well as the work done by the substance as it expands against the constant pressure.
Specific Heat at Constant Volume
The specific heat capacity at constant volume (CV) is the amount of heat energy required to increase the temperature of a substance by one degree Celsius or Kelvin while keeping the volume constant. CV only includes the heat energy required to raise the temperature of the substance since there is no expansion work being done against a constant volume.
Relation between CP and 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
- n is amount of substance
The value of the 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
- 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
The concept of specific heat capacity is used for the following below purposes,
- 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.
Also, Read
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
Q1: Define 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.
Q2: What is 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.
Q3: What is Heat Capacity Ratio?
Answer:
It is the ratio of two specific heat capacities, CP and CV is given by:
γ = Heat Capacity at Constant Pressure (CP)/ Heat capacity at Constant Volume (CV)
γ = CP / CV
Q4: How to Calculate 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
ΔQ = m c ΔT
Q5: What is 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.
Q6: What is Specific Heat Capacity of Ice, Water, and Steam?
Answer:
- Specific Heat Capacity of Ice is 2.108 kJ/kg-K
- Specific Heat Capacity of Water is 4.187 kJ/kg-K
- Specific Heat Capacity of Steam is 1.996 kJ/kg-K
Q7: What is Specific Heat Capacity of Air?
Answer:
The specific heat of air at constant pressure is 1.005 kJ/kg-K.
Q8: How Specific Heat of Gas is calculated?
Answer:
The Specific Heat of Gas is calculated by using the formula,
CP = CV + R
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