If you fill a container with air at room temperature (400 K), seal the container, and then heat the container to 500 K, what will the pressure be inside the container? Assume atmospheric pressure equal to 100,000 Pa.
To determine the pressure inside the container, we can use the ideal gas law, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Given:
Initial temperature (T₁) = 400 K
Final temperature (T₂) = 500 K
Atmospheric pressure (P₁) = 100,000 Pa (which is the initial pressure)
Volume (V) is constant
Ideal gas constant (R) = 8.314 J/(mol·K)
We can solve for the final pressure (P₂) using the formula:
P₂ = (P₁ * T₂) / T₁
Substituting the given values:
P₂ = (100,000 * 500) / 400
P₂ = 125,000 Pa
Therefore, the pressure inside the container, after heating it from 400 K to 500 K, will be 125,000 Pa.
To find the pressure inside the container after heating it, we can use the ideal gas law, which states that the product of pressure and volume is proportional to the product of the number of moles of gas and its absolute temperature.
The equation for the ideal gas law is:
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 (approximately 8.314 J/(mol·K))
T is the temperature in Kelvin
In this scenario, the volume and the number of moles of gas remain constant since the container is sealed. We are only changing the temperature and want to find the new pressure. Therefore, we can rewrite the equation as:
P1V1 / T1 = P2V2 / T2
where P1 is the initial pressure, V1 is the initial volume, T1 is the initial temperature, P2 is the final pressure, V2 is the final volume (which remains the same as the initial volume), and T2 is the final temperature.
Given:
P1 = atmospheric pressure = 100,000 Pa
V1 = V2 (volume remains constant)
T1 = 400 K
T2 = 500 K
Using these values, we can rearrange the equation and solve for P2:
P2 = (P1 * T2) / T1
Substituting the values:
P2 = (100,000 * 500) / 400
P2 = 125,000 Pa
Therefore, the pressure inside the container after heating it to 500 K would be 125,000 Pa.