Pressure within tyre

The first law of thermodynamics states that energy may be converted between forms, but cannot be created or destroyed. Joule was a superb experimentalist, and performed various types of work, each time generating energy in the form of heat. In one set of experiments, for example, he rotated small paddles immersed in a water trough and noted the rise in temperature. This experiment was apparently performed publicly in St Anne s Square, Manchester. Joule discerned a relationship between energy and work (symbol w). We have to perform thermodynamic work to increase the pressure within the tyre. Such work is performed every time a system alters its volume against an opposing pressure or force, or alters the pressure of a system housed within a constant volume. 

The inner liner forms the vital internal membrane which hold the inflation medium at an elevated pressure within the structure of the tyre. In early days... 

When a fully inflated car tyre is allowed to deflate, the air streaming through the nozzle is cold to the touch. The pressure of the air within the tyre is fairly high, so opening the tyre valve allows it to leave the tyre rapidly - the air movement may even cause a breeze. We could feel a jet of cold air on our face if we were close enough. As it leaves the tyre, this jet of air pushes away atmospheric air, which requires an effort. We say that work is performed. (It is a form of pressure-volume work, and will be discussed in more depth later, in Section 3.2.)... 

Alternatively, we could consider inflating the tyre with a series of, say, 100 short steps - each separated by a short pause. The difference in pressure before and after each of these small steps would be so slight that the gas within the tyre would be allowed to reach equilibrium with its surroundings after adding each increment, and before the next. Stated a different way, the difference between the pressure of the gas in the hand pump and in the tyre will always be slight. 

We can take this idea further. We need to realize that if there is no real difference in pressure between the hand pump and the gas within the tyre, then no work would be needed to inflate because there would never be the need to pump against a pressure. Alternatively, if the inflation were accomplished at a rate so slow that it was infinitesimally slow, then there would never be a difference in pressure, ensuring w was always zero. And if w was zero, then U would stay constant per increment. (We need to be aware that this argument requires us to perform the process isothermally.)... 

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