Why is the temperature constant in the following case:The piston for a bicycle pump is pushed slowing until pressure in pump increases. Temperature...

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.