Differences Between Kinetic Energy and Temperature

All objects in motion possess kinetic energy. The amount of ‘work’ required to overcome the stationary state of an object and bring it to motion is known as ‘Kinetic energy’. As the body starts moving, it gains ‘Kinetic Energy’ and maintains the same energy unless there is a change in its speed. The same amount of work is required to decelerate the moving body back to its stationary state. According to classical mechanics, any (non-rotating) object having translational motion will have kinetic energy equal to the product of one-half of the square of its velocity and mass.

Temperature is a physical quantity that describes how hot or cold a substance is. The direction of the spontaneous flow of heat energy from a hotter body (having higher temperature) to a cooler body (having lower temperature) is represented by Temperature. However, heat energy and temperature are not the same. Heat is a form of energy, whereas temperature measures how hot or cold a substance is. Temperature can be measured with the help of three scales:

1)    The Fahrenheit Scale

2)    The Celsius Scale

3)     The Kelvin Scale

1)    The Fahrenheit Scale

It is a scale used to measure temperature in Fahrenheit (°F). According to the Fahrenheit Scale, the freezing point of water is shown as 32°F, whereas the boiling point of water is shown as 212°F.

2)    The Celsius Scale

It is a scale used to measure temperature in Celsius or Centigrade (°C). According to the Celsius Scale, the freezing point of water is shown as 0°C, whereas the boiling point of water is shown as 100°C.

3)    The Kelvin Scale

It is a scale used to measure temperature in Kelvin (°K). According to the Kelvin Scale, the freezing point of water is shown as 273.15°K, whereas the boiling point of water is shown as 373.15°K.

All substances are composed of molecules in motion possessing some kinetic energy. The motion of each of these molecules vary. Various factors affect this motion of molecules. But, does temperature affect kinetic energy? 

Does Temperature Affect Kinetic Energy?

The kinetic theory of gases can explain how kinetic energy and temperature are related and how does temperature affect kinetic energy?

 The kinetic theory of gases states that all gases are composed of microscopic particles that tend to move in straight lines unless they collide with other gaseous molecules or an object. 

 Consider a burning candle. Its flame makes the surrounding environment warmer. The air molecules in the proximity of the flame gain energy from the flame, and they start to move around faster. This transfer of energy causes the collision of the air molecules, which releases heat. As a result, the temperature of the surrounding environment becomes higher. 

It is common knowledge that a fire will warm up a room faster than a burning candle. This is because the fire can transfer more amount of energy to the surrounding environment. As a result, the molecules in the air in proximity to the fire will move much faster and cause more collisions as compared to the burning candle.

Or, consider a container containing only water vapour molecules with an attached thermometer. The water vapour molecules will be in motion in the container. On increasing the temperature of the container, the motion of molecules will increase. The collision among the molecules and their collision with the container will increase. On decreasing the temperature of the container, the gas molecules will move more slowly.

Not all molecules in a system have the same kinetic energy. However, most of the gas molecules will have the average kinetic energy.

As the speed of the gas molecules increases, more collisions occur, and the total kinetic energy of the gas molecules also increases. It is impossible to measure the speed of kinetic energy of each gas molecule. Instead, the average kinetic energy of a gas is measured as a function of temperature.

Kinetic Energy And Temperature Formula 

 As stated above, the average kinetic energy of a gas is measured as a function of temperature. Let 1g molecule of gas with volume and temperature be V and T respectively and number of molecules of 1 mol of gas (NA) = 6.02 × 1023 molecules. According to kinetic theory of gases, the pressure of gas for 1 g molecules is.

P=13mNAVv2

PV=13mNAv2 …….eq(1)

Where m is mass of molecule and v2 is root mean square speed.

By using ideal gas equation in eq.(1)

RT=13mNAv2

v2 =3RTmNA…..eq(2)

Now Averge kinetic energy for each molecule is 

E=12mv2

Now by using eq(1)

E=12m3RTmNA

E=32(RNA)T

Since RNA=kb which is Boltzman constant So

E=32kBT

Above equation is a relation between the average kinetic energy of each molecule and temperature.

Not all molecules in a system have the same kinetic energy. However, most of the gas molecules will have the average kinetic energy. With the help of equation (3), if Boltzmann constant and temperature (in K) is known, the temperature of even one molecule can be figured out.

ASPECTS OF KINETIC ENERGY AND TEMPERATURE

The aspects of kinetic energy and temperature can be better explained with the help of the kinetic molecular theory of gases.

Kinetic molecular theory of gases states that the average kinetic energy of a gas is measured as a function of temperature. Whenever a substance is heated, the energy absorbed by the substance gets stored within the particles, whereas some energy is utilised to increase the motion of the particles within the substance. 

This is identified by the increase in the temperature of the substance. Kinetic energy is the characteristic property of objects in motion, whereas temperature is a consequence of the movements and collision of molecules of an object.

Consider two beakers containing hot and cold water, respectively. When some dye is poured into both the containers, it will be observed that the dye will spread inside the beaker containing hot water much faster than the beaker having cold water. This is because of increased molecular motions in the beaker having hot water. Increased kinetic energy of the molecules due to temperature increases interactions and collisions between the molecules.

CONCLUSION

All objects in motion possess kinetic energy. The amount of ‘work’ required to overcome the stationary state of an object and bring it to motion is known as ‘Kinetic energy’. Temperature is a physical quantity that describes how hot or cold a substance is.  But does temperature affect kinetic energy?

Yes, they are directly related to each other. The motion of the molecules increases by increasing the temperature of a gas. As the speed of the gas molecules increases, more collisions occur, and the total kinetic energy of the gas molecules also increases. It is impossible to measure the speed of kinetic energy of each gas molecule. Instead, the average kinetic energy of a gas is measured as a function of temperature.