# For a gas, which variables are inversely proportional to each other if all other conditions are held constant?a. pressure and temperature b. volume and temperature c. pressure and volume d....

For a gas, which variables are inversely proportional to each other if all other conditions are held constant?

a. pressure and temperature

b. volume and temperature

c. pressure and volume

d. pressure, temperature, and volume

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### 1 Answer

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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