Derive the relations for pressure and temperature in terms of average
kinetic energy of the molecules?
Answers
Answer:
As the number of molecules increases, the number of collisions and thus the pressure increase. ... We can derive a relationship between temperature and the average translational kinetic energy of molecules in a gas. Recall the previous expression of the ideal gas law: PV = NkT.
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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.
Our sense of temperature is related to heat flow. If two bodies are at the same temperature and put in thermal contact, no heat flow between them occurs. If there is a temperature difference, heat flow will occur until both bodies are at the same temperature.
According to kinetic theory, the flow of internal energy in the form of heat will occur between two bodies only if there is a difference in the average translational kinetic energy of the molecules of each body.
It is only the average molecular translational kinetic energy that determines temperature - that is the average kinetic energy of the motion of the centres of mass of the molecules. Vibration and rotation of molecules do not contribute to temperature directly.