Question

Consider two different processes (a) You are preparing for a bike race, and you note that the pressure in your tires is only 80 psi (5 atmospheres). For optimal performance, however, you want your tires to be at 160 psi. When you inflate the tire with a hand pump, the temperature inside the tire rises. (You can only really feel the warming effect at the metal valve stem since the rubber in the tire and tube is a good insulator.) (b) Artificial snow is made by quickly releasing a mixture of compressed air and water at about 20 atm from a snow making machine to the surroundings. Explain these results two different ways: (1) In terms of the First Law of Thermodynamics, and: (2) In terms of the ideal gas equation, assuming air behaves like an ideal gas.

Answer 1

a)

The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.

It states that the change in the internal energy ΔU of a closed system is equal to the amount of heat Q supplied to the system, minus the amount of work W done by the system on its surroundings.

In part 1, when you inflate the tire with hand pump,Q - heat supplied to the system is used to inflate the tire and increase the internal energy of the system. The change in energy ΔU is given by ΔU = CΔT, where C is the proportionality constant. The increase in the internal energy of the system increases the temperature of the tire.

P V = n R T is the ideal gas equation. In case 1 when tire is inflated, the pressure and volume increases, therefore since temperature is directly proportional, it also increases.

b)

Usiing first law of thermodynamics, equation ΔU = Q + W. A snowmaking machine contains a mixture of compressed air and water vapor at about 20 atm. Because of the large difference in pressure between the tank and the outside atmosphere, when the mixture is sprayed into the atmosphere it expands so rapidly that, as a good approximation, no heat exchange occurs between the system (air and water) and its surroundings; that is, Q = 0. (In thermodynamics, such a process is called an adiabatic process.) Thus, we write ΔU = Q + W = W.

Because the system does work on the surroundings, W is a negative quantity, and there is a decrease in the system’s energy. The change in energy ΔU is given by ΔU = CΔT, where C is the proportionality constant. Because ΔU is negative, ΔT must also be negative, and it is this cooling effect (or the decrease in the kinetic energy of the water molecules) that is responsible for the formation of snow.

Using ideal gas equation, as the mixture is released, the pressure decreases which again is directly proportional to the temperature, hence the temperature decreases, resulting in the formation of snow.