To determine the pressure of the gas at 20°C after it is cooled from 60°C, we can make use of the ideal gas law, which states:
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 in Kelvin
Since the container is sealed and rigid, the volume (V) remains constant. We can assume that the number of moles (n) of gas also remains constant.
To solve for the pressure (P) at 20°C, we need to convert both temperatures to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.
Given: Initial pressure (P1) = 3.5 ATM Initial temperature (T1) = 60°C = 60 + 273.15 = 333.15 K Final temperature (T2) = 20°C = 20 + 273.15 = 293.15 K
Now, we can set up the following equation using the initial and final conditions:
P1 * T1 = P2 * T2
Substituting the known values:
3.5 ATM * 333.15 K = P2 * 293.15 K
Simplifying the equation:
P2 = (3.5 ATM * 333.15 K) / 293.15 K
Calculating:
P2 ≈ 3.964 ATM
Therefore, the pressure of the gas at 20°C is approximately 3.964 ATM.