The ideal gas law states `pV=NkT` where p is the pressure in atmospheres, V is the volume in liters, N is the number of particles, k is Boltzmann's constant, and T is the absolute temperature.

(a) pressure and temperature: From the equation it is apparent that as p increases, T must also increase to keep the equation balanced. (Assuming V,N, and k are held constant). Thus p and T are directly proportional. This agrees with intuition: as the temperature increases in a sealed pan, the pressure increases and vice versa.

(b) volume and temperature: As in (a), an increase in volume requires an increase in temperature to maintain the balance of the equation. This also agrees with intuition -- increasing the temperature increases the volume.

(c) pressure and volume: From the equation these are inversely proportional. If you increase the pressure, the volume must decrease proportionally to maintain the equations balance. This agrees with intuition -- if you squeeze a container the volume will be reduced.

(d) pressure, temperature and volume: as you increase the pressure and temperature, the volume must increase to maintain the equation's balance, so the variables are directly proportional.

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**The answer is (c) the pressure is inversely proportional to the
volume assuming the number of particles and temperature are held
constant.**

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