Pressure volume graph for two processes. An explintion would be greatly apprecia

Question

Pressure volume graph for two processes. An explintion would be greatly appreciated

Two processes a b and c d are shown on the pressure versus volume graph. A sample of an ideal gas is expanded using process a b, and an identical sample is expanded using process c d. A student trying to decide which gas has the greatest change in temperature states: "The change in pressure is the same for both processes, and the change in volume is greater for process c d. So the change in temperature must be greater for process c d. " What, if anything, is wrong with the student's contention? If something is wrong, identify it and explain how to correct it. If nothing is wrong, explain the physics behind the student's answer.

Explanation / Answer

Student's answer is correct......here is the explanation

First lets talk about temperature- one definition of temperature is " A measure of the average kinetic energy of the particles in a sample of matter". So if the average kinetic energy of the molecules goes up, the temperature goes up. Now let's look at gas in a balloon. Inside, the particles (atoms, molecules) are continuously colliding with each other, and the surface of the balloon. If you have a fixed number of particles, and they sped up (i.e higher kinetic energy or temperature)they would collide at higher energy with both each other and the surface of the balloon which would force it outward or expand. What happens if I had a container of gas and suddenly crushed it to half it's volume? Since the gas has nowhere to go, the density of the gas goes up and the particles are hitting each other (and the walls with greater frequency-so the temperature goes up. This is the principle on diesel engines work. (diesel's don't use spark plugs)- the compression of the fuel-air mix causes it to ignite.
There is an equation called Van Der Wals equation of state (or something similar) which was derived from Boyles Law and Charles Law which says that for a given system, (Pressure X Volume)/Temperature is constant. Or, in other terms, Initial PV/T=Final PV/T. If you change either P V, or T, the other factors will change to keep PV/T constant. Hope this helps.

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