Why is the temperature constant in the following case:
The piston for a bicycle pump is pushed slowing until pressure in pump increases. Temperature remains the same. Moving the piston very slowly ensures that the enclosed air remains at the same temperature. Explain why this is so and state its effect on the average speed of the molecules.
According to the ideal gas law P*V = n*R*T, where P is the pressure, V is the volume, n is the amount of the gas, R is the gas constant and T is the temperature.
Now the piston of the pump is pushed and the pressure increases slowly. We see that the terms on the left hand side of the ideal gas law, which are pressure and volume are changing. Pressure is increasing and the Volume is decreasing. There is no change in the Temperature when the piston is pushed in slowly as there is enough time for the heat generated to get dissipated. The speed of the molecules also remains the same as due to the escape of heat, there is no increase in temperature.
If the piston was pushed in fast enough, or the piston was insulated to prevent any escape of heat, there would have been an increase in temperature.
But as the piston is pushed in slowly, no change is seen in the temperature and the effect of the increase in pressure is canceled by the decrease in volume.