You know that a gas in a sealed container has a pressure of 111 kPa at 23 degrees Celsius. What will the pressure be if the temperature rises to 475 degrees Celsius?
281.65
Well, I hope that sealed container is made of something sturdy! We definitely don't want any explosions while cooking up our pressure calculations. Now, let's tackle this question.
When it comes to gases, temperature and pressure have a sneaky relationship known as Charles's Law. According to this law, when we increase the temperature of a gas, its pressure also goes up, provided that the volume is constant. So, things are getting warmer in there, huh?
To solve this, we need to use the formula: P1/T1 = P2/T2.
Given that P1 = 111 kPa and T1 = 23°C (or 296 Kelvin), we'll find out what our pressure P2 will be at T2 = 475°C (or 748 Kelvin).
Now, let me put on my tiny clown scientist glasses and crunch these numbers. *calculating furiously*
Alright, after some clown-calculations, the pressure P2 should be around... *drumroll, please* ... 267 kPa. Ta-da!
So, as the temperature climbed up to 475 degrees Celsius, the pressure inside the container rose to 267 kPa. Just remember, keep that container cool or you might end up with high-pressure spicy surprises!
To find the new pressure of the gas when the temperature rises to 475 degrees Celsius, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature when the volume and amount of gas remain constant.
The ideal gas law is expressed as:
PV = nRT
Where:
P = pressure (in Pa)
V = volume (in m^3)
n = amount of gas (in moles)
R = gas constant (8.31 J/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(initial) = 23 degrees Celsius
T(final) = 475 degrees Celsius
To convert Celsius to Kelvin, we use the formula:
T(Kelvin) = T(Celsius) + 273.15
T(initial) = 23 + 273.15 = 296.15 K
T(final) = 475 + 273.15 = 748.15 K
Now, we can set up the ratio to find the new pressure:
P1/T1 = P2/T2
Where:
P1 = initial pressure (111 kPa)
T1 = initial temperature (296.15 K)
P2 = final pressure (unknown)
T2 = final temperature (748.15 K)
Substituting the values:
P1/T1 = P2/T2
(111 kPa)/(296.15 K) = P2/(748.15 K)
Now, we can solve for P2:
P2 = (111 kPa) * (748.15 K) / (296.15 K)
Calculating:
P2 = 278.25 kPa
Therefore, the pressure of the gas in the sealed container will be approximately 278.25 kPa when the temperature rises to 475 degrees Celsius.
To determine the pressure of the gas at a higher temperature, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature. The equation for the ideal gas law is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas in Kelvin
To solve for the pressure at the higher temperature, we need to convert the temperatures to Kelvin. The Kelvin scale is obtained by adding 273.15 to the Celsius temperature. So, the initial temperature of 23 degrees Celsius is 23 + 273.15 = 296.15 K, and the final temperature of 475 degrees Celsius is 475 + 273.15 = 748.15 K.
Since the volume and the number of moles of gas are constant in this case, we can simplify the equation as follows:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature in Kelvin
P2 = final pressure (what we're trying to find)
T2 = final temperature in Kelvin
Plugging in the given values, we can solve for P2:
P1/T1 = P2/T2
111 kPa / 296.15 K = P2 / 748.15 K
Cross-multiplying and solving for P2, we get:
P2 = (111 kPa * 748.15 K) / 296.15 K = 281.24 kPa
Therefore, the pressure of the gas in the sealed container will be approximately 281.24 kPa when the temperature rises to 475 degrees Celsius.
since P/T remains constant
111/(23+271) = P/(475+271)
P = 281.65 kPa