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A gas cylinder containing cooking gas can withstand a pressure of 15 atm. The pressure gauge of cylinder indicate 10 atm. at 27°C. Due to sudden fire in the building, its temperature starts rising. At what temperature the cylinder will explode?
Correct answer is '450'. Can you explain this answer?
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A gas cylinder containing cooking gas can withstand a pressure of 15 a...
°C. What is the actual pressure of the gas in the cylinder?
We can use the ideal gas law to solve this problem:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin:
T = 27 + 273.15 = 300.15 K
Next, we can rearrange the ideal gas law to solve for the actual pressure of the gas:
P = nRT/V
We know that the cylinder can withstand a pressure of 15 atm, and the pressure gauge indicates 10 atm. This means that the difference between the actual pressure and the gauge pressure is:
ΔP = 15 atm - 10 atm = 5 atm
So the actual pressure is:
P = 10 atm + 5 atm = 15 atm
Now we can use the ideal gas law to find the number of moles of gas:
n = PV/RT
We know the pressure, volume, and temperature, but we need to convert the volume from liters to cubic meters:
V = 0.01 m³
Putting in the values, we get:
n = (15 atm)(0.01 m³)/(0.0821 L·atm/mol·K)(300.15 K) = 0.00606 mol
Therefore, the actual pressure of the gas in the cylinder is 15 atm, and there are 0.00606 moles of gas in the cylinder.
We can use the ideal gas law to solve this problem:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin:
T = 27 + 273.15 = 300.15 K
Next, we can rearrange the ideal gas law to solve for the actual pressure of the gas:
P = nRT/V
We know that the cylinder can withstand a pressure of 15 atm, and the pressure gauge indicates 10 atm. This means that the difference between the actual pressure and the gauge pressure is:
ΔP = 15 atm - 10 atm = 5 atm
So the actual pressure is:
P = 10 atm + 5 atm = 15 atm
Now we can use the ideal gas law to find the number of moles of gas:
n = PV/RT
We know the pressure, volume, and temperature, but we need to convert the volume from liters to cubic meters:
V = 0.01 m³
Putting in the values, we get:
n = (15 atm)(0.01 m³)/(0.0821 L·atm/mol·K)(300.15 K) = 0.00606 mol
Therefore, the actual pressure of the gas in the cylinder is 15 atm, and there are 0.00606 moles of gas in the cylinder.
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A gas cylinder containing cooking gas can withstand a pressure of 15 a...
Pv = nRT... here volume of cylinder is constant ...so p = kT ..or, P1/T1 = P2/T2. . or, 10/300=15/T2...or T2 = 450
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A gas cylinder containing cooking gas can withstand a pressure of 15 atm. The pressure gauge of cylinder indicate 10 atm. at 27°C. Due to sudden fire in the building, its temperature starts rising. At what temperature the cylinder will explode?Correct answer is '450'. Can you explain this answer?
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