A gas in a sealed container has a pressure of 50 kPa at 27°C.
What will the pressure of the gas be if the temperature rises to 87°C?
Pressure: 50(87+273)/273
This is Charles' Law.
To determine the pressure of the gas at 87°C, we can use the ideal gas law equation: 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 in Kelvin.
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature, T₁ = 27°C + 273.15 = 300.15 K
Final temperature, T₂ = 87°C + 273.15 = 360.15 K
Given:
Initial pressure, P₁ = 50 kPa
Final pressure, P₂ = ?
We can assume that the volume and number of moles of the gas remain constant (since the container is sealed).
Now, we can set up the following equation using the ideal gas law:
P₁V₁ / T₁ = P₂V₂ / T₂
Since the volume and number of moles of the gas remain constant, we can cancel them out from the equation. Thus, we are left with:
P₁ / T₁ = P₂ / T₂
Substituting the given values, we have:
50 kPa / 300.15 K = P₂ / 360.15 K
Now, we can rearrange the equation to solve for P₂:
P₂ = (50 kPa / 300.15 K) * 360.15 K
P₂ ≈ 60.03 kPa
Therefore, the pressure of the gas will be approximately 60.03 kPa when the temperature rises to 87°C.
To determine the pressure of the gas at a higher temperature, we need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure. This is expressed by the equation:
(V1 / T1) = (V2 / T2)
Where:
V1 is the initial volume of the gas,
T1 is the initial temperature of the gas,
V2 is the final volume of the gas, and
T2 is the final temperature of the gas.
Since the problem states that the gas is in a sealed container, we can assume that the volume is constant. Therefore, the equation can be simplified to:
(T1 / P1) = (T2 / P2)
Where:
P1 is the initial pressure of the gas, and
P2 is the final pressure of the gas.
Plugging in the given values:
T1 = 27°C + 273.15 (converting to Kelvin) = 300.15 K
P1 = 50 kPa
T2 = 87°C + 273.15 = 360.15 K
Using the equation, we can solve for P2:
(T1 / P1) = (T2 / P2)
P2 = (T2 * P1) / T1
P2 = (360.15 K * 50 kPa) / 300.15 K
Now, we can proceed with the calculation:
P2 = (18007.5 kPa*K) / 300.15 K
P2 ≈ 60.0 kPa
Therefore, at a temperature of 87°C, the pressure of the gas in the sealed container will be approximately 60.0 kPa.