A certain type of ideal gas at pressure p0 is contained in a plugged flask of volume V initially at temperature T1 . The environmental pressure remains constant p0 .
(a) As the flask is heated up to temperature T2 , the plug pops out. What is the pressure p2 of the ideal gas inside of the flask right before the plug pops out?
(b) Following the preceding part, the plug is put back on once the pressure of the ideal gas becomes balanced with the environmental pressure p0 , which is assumed to be constant. Remove the flask from heat and let it cool down to the initial temperature T1 . What is the pressure p3 of the ideal gas in the flask now?
(c) Order p2,p3,andp0 in magnitude. Does it make sense? How to use this observation to tell wheter there is loss of gas when the plug pops out and to decide how much gas is lost?
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
(a) To find the pressure p2 of the ideal gas inside the flask right before the plug pops out, we can assume that the number of moles of gas remains constant. Therefore, we can set up the equation:
p0 * V = n * R * T1
Rearranging the equation, we have:
p0 = (n * R * T1) / V
Now, using the same equation for the final state, right before the plug pops out at temperature T2, we have:
p2 * V = n * R * T2
Rearranging the equation, we have:
p2 = (n * R * T2) / V
Thus, the pressure p2 right before the plug pops out is given by (n * R * T2) / V.
(b) After the plug pops out, the pressure inside the flask will equilibrate with the environmental pressure p0. So, when the plug is put back on, the pressure of the ideal gas becomes equal to p0. Therefore, p3 = p0.
(c) To determine the order of magnitude for p2, p3, and p0, we need more information about the temperatures T1 and T2 and the volume V. Without this information, we cannot determine the order of magnitude.
Observation of the pressures can give insights into whether there is a loss of gas when the plug pops out and how much gas is lost. If the pressure p2 right before the plug pops out is significantly higher than p0, it suggests that some gas has escaped. If p3 equals p0 after the flask is cooled down, it suggests that no additional gas has been lost during the process.
However, to quantify the amount of gas lost, we would need to know the initial number of moles of gas (n) and other relevant information about the setup, such as volume changes or changes in the number of moles of gas during heating and cooling. Without this information, it is not possible to determine the amount of gas lost with certainty.