Explain the following phenomena according to the first law of thermodynamics. (a) When a bicycle tire is inflated with a hand pump, the temperature inside rises. You can feel the warming effect at the valve stem. (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.

a) The process can be modeled as an adiabatic compression, because the pulses of pressurized air is governed into the tire and time frame is very small for any heat transfer through the tires. Hence, Q_net = 0.

The first law of thermodynamics states that the change in the internal energy is ∆U=Q-W= -W, since Q_net = 0 for adiabatic processes. Work is being done on the system by pumping action hence W_net is negative; therefore the change in the internal energy, ∆U, is positive. Since ∆U, is a function of initial and final temperatures the final final temperature must increase for ∆U to be positive.

b) The process can be modeled as an adiabatic expansion when a highly pressurized mixture of air and water is released into atmosphere from 20 atm to 1 atm. The time frame is very small for any heat transfer through the mixture. Hence, Q_net = 0.

The first law of thermodynamics states that the change in the internal energy is ∆U=Q-W= -W, since Q_net = 0 for adiabatic processes. Work is being done by the mixture on its surroundings due to change in pressure from high to low. The W_net is positive; therefore the change in the internal energy, ∆U, is negative. Since ∆U, is a function of initial and final temperatures the final final temperature must decrease for ∆U to be negative. The final temperatures drops below freezing point due to sudden adiabatic expansion of mixture leads to formation of snow.