What happens to the pressure inside a gas-filled ball when the temperature is increased? Explain your answer, stating the assumption made.

From definition of pressure have P=F/A (in reality for a ball we are talking about infinitesimal areas, but the general definition is sufficient at this level). Assume that the area of the surface under consideration stays fixed. This is an important point about physics in general as we must be aware of what assumptions are being made and if they are appropriate. This effectively means the shape of the ball stays fixed and so we can allow proportionality between P and F. By Newton II Law we know F=dp/dt and so combining equations have P=(1/A)dp/dt. Stating conservation of momentum in a collision and the assumption of infinite wall mass, and the kinetic definition of temperature (proportional to average particle kinetic energy sufficient). Hence an increase in temperature leads to an increased rms particle velocity, leading to an increased average particle momentum. Hence the overall pressure is increased as we observe a higher collision rate and a higher change in momentum per collision.