What is the relation between kinetic energy of particles and temperature?
Answers
Another way of thinking about temperature is that it is related to the energy of the particles in the sample: the faster the particles are moving, the higher the temperature. It may well take different amounts of energy to get particles moving at the same average kinetic energy.
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Answer:
Kinetic energy is the energy possessed by a substance/body by virtue of its motion.
For example if I am allowing a ball to freely fall under gravity the potential energy(Energy possessed by body by virtue of its position) will change to kinetic energy. That is when body has motion it has kinetic energy given by formula E=0.5mV^2, where m=mass and V= velocity.
Coming to your question, kinetic energy is related with temperature. If temperature is increased kinetic energy is increased and vice-versa. HOW?
Consider a gas which is filled inside a container. Let it be at room temperature. Let u consider that the gaseous molecules will have less interaction at this stage. Now slowly we increase the temperature. The gaseous molecules starts to gain energy from the heat being supplied , because of which the heat energy is converted to internal energy(Let us not consider the losses at the moment). This internal energy is the sum of potential energy ,kinetic energy vibration etc. Hence the kinetic energy increases because of which the molecules start colliding with each other and and because of this collision the temperature increases.
Temperature is directly proportional to the kinetic energy of the atoms that a body is made of. This relation is valid concerning the velocities relative to the center of mass of the body. In other words, concerted movements like translation and rotation do not affect temperature.
The relation is given by <Katoms>=dN2×kB×T where T is the temperature, kB a physical constant, d the degrees of liberty of your atoms (set as 3 in most cases, for the 3 coordinates of space) and <Katoms> the mean kinetic energy of all the atoms (the mean of the momentum squared and divided by twice the mass of each atom).
This kinetic energy must not be mistaken with the kinetic energy of the full system. As I said, this relation is valid in a referential in which the body is in uniform motion. So any movement the whole body does not raise its temperature. It must be emphasized that the atoms are moving even when the body is at rest. So <Katoms>≠Kbody and Kbody=p22m where p is the momentum of the body and m its mass.