Final answer:
To calculate the pressure of a gas, you can use the ideal gas law equation P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. By substituting the given values into the equation and solving for the final pressure, we find that the final pressure of the gas is approximately 1036.8 atm.
Step-by-step explanation:
Calculation of the Pressure of a Gas
Given:
Initial temperature (T1) = 360 K
Final temperature (T2) = 500 K
Initial volume (V1) = V
Final volume (V2) = 4V
Solution:
Step 1: Apply Charles's Law to find the relationship between temperature and volume at constant pressure: V1/T1 = V2/T2
Step 2: Substitute the given values into the equation: V1/360 = 4V/500
Step 3: Cross multiply and solve for V: 500V1 = 4V × 360
Step 4: Simplify the equation: 500V1 = 1440V
Step 5: Divide both sides by 1440 to solve for V: V = 500V1/1440
Step 6: Substitute the value of V in the equation for final volume: V2 = 4(500V1/1440)
Step 7: Simplify the equation: V2 = 2000V1/1440
Answer:
The final volume of the gas is 2000V1/1440.
Now, to calculate the final pressure, we can use the equation for the ideal gas law: 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.
Since the number of moles and the ideal gas constant remain constant, we can rewrite the equation as P1V1 = P2V2.
We're given the initial pressure (P1) as 1 atm and the initial volume (V1) as V. We already found the final volume (V2) as 2000V1/1440.
Substituting these values into the equation, we get P1V1 = P2(2000V1/1440).
To solve for the final pressure (P2), we can rearrange the equation to isolate P2: P2 = (P1V1)/(2000V1/1440).
Simplifying the equation, P2 = (1 atm × V)/(2000 × V1/1440)
= 1440 atm/(2000/1440).
Calculating the result, we get P2 = 1036.8 atm.
Therefore, the final pressure of the gas is approximately 1036.8 atm.