A cylinder of acetylene gas is kept at a temperature of 291K. The pressure in the cylinder is 5atm. This cylinder can withstand a pressure of 8atm before it explodes. What is the maximum temperature that the cylinder can safely be stored at ?
Well, you certainly don't want the cylinder to "blow its top," do you? That would be quite an explosive situation! Now, let's calculate the maximum temperature that would keep the cylinder from going kaboom.
We can use the ideal gas law equation here: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. Since we are looking for the maximum temperature, we'll rearrange the equation as T = PV / (nR).
Given that the pressure before explosion is 8 atm and the pressure inside the cylinder is 5 atm, we can set up the equation as follows:
8 atm x V = 5 atm x V
Since the volume is constant, we can cancel it out. Now, we have:
8 atm = 5 atm
Hmm, that's a bit strange. It seems like the pressure inside the cylinder is below the explosion threshold. So, no matter what the temperature is, the cylinder should be safe to store!
But hey, let's not forget that safety is always the top priority. Make sure to handle cylinders with care and consult the relevant guidelines or experts to ensure proper storage conditions. Safety first, my friend!
To find the maximum temperature that the cylinder can safely be stored at, we can use Charles's Law. Charles's Law states that for a fixed amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature.
The formula for Charles's Law is: V1/T1 = V2/T2
Where:
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature
Given:
Initial pressure (P1) = 5 atm
Final pressure (P2) = 8 atm
Since the volume is constant, we can rewrite Charles's Law as: P1/T1 = P2/T2
Solving for T2 (the maximum temperature):
T2 = (P2 * T1) / P1
Substituting the given values:
T2 = (8 atm * 291 K) / 5 atm
Calculating:
T2 = 4656 K / 5 atm
T2 = 931.2 K
Therefore, the maximum temperature that the cylinder can safely be stored at is 931.2 K.
To determine the maximum temperature at which the cylinder can be safely stored, we need to consider the ideal gas law, which states:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Since we are interested in the maximum temperature that the cylinder can withstand, we can rearrange the equation to solve for temperature:
T = PV / (nR)
To find the temperature, we need to know the number of moles (n) of acetylene gas in the cylinder. Unfortunately, this information is not given in the question. Without the number of moles, we cannot determine the maximum temperature of the cylinder.
It is important to note that the maximum pressure (8 atm) mentioned in the question is irrelevant for calculating the maximum temperature. The maximum pressure given is the limit before the cylinder explodes, not a limit that determines the temperature.