Why is the pressure of a gas directly proportional to temperature?

Why is the pressure of a gas directly proportional to temperature?

• A. P1/T1 = P2/T2....because as temperature increases, KE increases, which makes collisions happen more often and harder
• B. P1 x T1 = P2 x T2
• C. P1/T1 = P2+T2
• D. P1 - T1 = P2 - T2

Answer: (A)

Direct proportionality between pressure and temperature comes from how gas molecules move: at a fixed amount of gas in a fixed volume, raising the temperature increases the average kinetic energy of the molecules. Faster molecules collide with the container walls more often and with greater force, so the pressure rises. This relationship is expressed by P ∝ T, which for two states is written as P1/T1 = P2/T2 when the volume and amount of gas are unchanged. It’s important to use Kelvin so the temperature scale starts at absolute zero; if Celsius were used, the simple proportionality would not hold across all temperatures. The other algebraic forms don’t reflect a direct proportionality between P and T, so they don’t describe the observed behavior.

Direct proportionality between pressure and temperature comes from how gas molecules move: at a fixed amount of gas in a fixed volume, raising the temperature increases the average kinetic energy of the molecules. Faster molecules collide with the container walls more often and with greater force, so the pressure rises. This relationship is expressed by P ∝ T, which for two states is written as P1/T1 = P2/T2 when the volume and amount of gas are unchanged. It’s important to use Kelvin so the temperature scale starts at absolute zero; if Celsius were used, the simple proportionality would not hold across all temperatures. The other algebraic forms don’t reflect a direct proportionality between P and T, so they don’t describe the observed behavior.