To determine the final temperature of a gas when it is compressed, we can use the ideal gas law equation:
PV = nRT
Where: P is the pressure of the gas V is the volume of the gas n is the number of moles of gas R is the ideal gas constant T is the temperature of the gas in Kelvin
First, let's convert the initial temperature from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius value.
Initial temperature (in Kelvin) = 0°C + 273.15 = 273.15 K
Since the container is compressed to half of its original volume, the new volume will be 500 ml divided by 2, which is 250 ml or 0.25 L.
We assume the number of moles and the amount of gas remains constant, so n and R can be considered constant as well.
The initial pressure (P1) and temperature (T1) are known, and we want to find the final temperature (T2).
Using the initial and final conditions, we can set up the equation as follows:
P1V1 / T1 = P2V2 / T2
Substituting the known values: P1 = P2 (since the amount of gas is constant) V1 = 500 ml = 0.5 L T1 = 273.15 K V2 = 250 ml = 0.25 L
The equation becomes: P1 * V1 / T1 = P2 * V2 / T2
Simplifying the equation: P1 * V1 * T2 = P2 * V2 * T1
Since P1 = P2, the equation becomes: V1 * T2 = V2 * T1
Substituting the known values: 0.5 L * T2 = 0.25 L * 273.15 K
Solving for T2: T2 = (0.25 L * 273.15 K) / 0.5 L
T2 = 136.575 K
Therefore, when the gas is compressed to half of its original volume, its temperature would be approximately 136.575 Kelvin.