Gases and the absolute scale of temperature

1. Convert Temperatures to Kelvin:
T₁ = 27°C + 273 = 300 K
T₂ = 327°C + 273 = 600 K

2. Apply the Pressure Law (P₁/T₁ = P₂/T₂):
(1.0 x 10⁵ Pa) / 300 K = P₂ / 600 K

3. Solve for P₂:
P₂ = (1.0 x 10⁵ Pa * 600 K) / 300 K
P₂ = 2.0 x 10⁵ Pa

*Explanation: The pressure increases because the increased temperature gives the gas particles more kinetic energy, causing them to collide with the container walls more frequently and with greater force.*

When the volume is increased, the gas particles have more space to move around. This means they collide with the walls of the container less frequently. As the number of collisions per second decreases, the pressure decreases. The average kinetic energy and speed of the particles remains the same because the temperature is constant.

T(K) = θ(°C) + 273
T(K) = 27 + 273
T(K) = 300 K

Explanation: To convert from Celsius to Kelvin, add 273 to the Celsius temperature.

The Kelvin scale is an absolute temperature scale, meaning that 0 K corresponds to absolute zero, the point at which all molecular motion ceases. If Celsius were used, calculations could produce negative pressures (e.g. volume and pressure are directly proportional in kelvin, but are not in celsius). Also, using Celsius would produce errors in calculations involving the gas laws, because the relationships between variables such as pressure, volume, and temperature are only directly proportional when temperature is expressed in Kelvin.

Formula: P₁V₁ = P₂V₂
Working: P₂ = (P₁V₁) / V₂ = (1.0 x 10⁵ Pa * 2.0 m³) / 0.9 m³ = 2.22 x 10⁵ Pa
Answer: 2.22 x 10⁵ Pa. The pressure increases because the same number of gas molecules are now in a smaller space, leading to more frequent collisions with the container walls.

When the volume decreases, the gas molecules have less space to move in. This means they collide more frequently with the walls of the container. The increased frequency of collisions results in a greater force exerted on the walls per unit area, hence the pressure increases. The temperature is constant, therefore the average kinetic energy of the molecules remains constant.