What is the final pressure of the gas relative to its initial pressure when there is an increase in Kelvin temperature of a cylinder of compressed gas by a factor of 2.7?
To determine the final pressure of the gas relative to its initial pressure when there is an increase in Kelvin temperature by a factor of 2.7, we can use the ideal gas law. The ideal gas law equation is given as:
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
At constant volume, the equation simplifies to:
P1/T1 = P2/T2
Where:
P1 is the initial pressure
T1 is the initial temperature
P2 is the final pressure
T2 is the final temperature
From the question, we know that the Kelvin temperature has increased by a factor of 2.7. Let's call the initial temperature T1 and the final temperature T2. We can write:
T2 = 2.7 * T1
Now we can substitute the values into the equation:
P1/T1 = P2/(2.7 * T1)
To isolate P2, we can cross-multiply:
P2 = P1 * 2.7
Therefore, the final pressure of the gas relative to its initial pressure is 2.7 times the initial pressure.