A balloon is filled to 1.000L at the bottom of the Marianas Trench, where the pressure exerted on it is 1065 atm and the temperature is 2°C, and taken to Columbus, where the pressure is 0.967 atm and the temperature is 30.00°C. What is its new volume?
To find the new volume of the balloon, we can use the combined gas law equation, which relates the initial and final conditions of pressure, temperature, and volume.
The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (at the bottom of the Marianas Trench) = 1065 atm
V1 = initial volume = 1.000 L
T1 = initial temperature = 2°C + 273.15 (converted to Kelvin) = 275.15 K
P2 = final pressure (in Columbus) = 0.967 atm
T2 = final temperature = 30.00°C + 273.15 (converted to Kelvin) = 303.15 K
V2 = final volume (what we want to find)
Now, let's plug in the values into the equation and solve for V2:
(P1 * V1) / T1 = (P2 * V2) / T2
(1065 atm * 1.000 L) / 275.15 K = (0.967 atm * V2) / 303.15 K
Simplifying the equation:
1065 L * K / 275.15 = 0.967 atm * V2 /303.15 K
Cross multiplying:
(1065 L * K * 303.15 K) / (275.15 K) = 0.967 atm * V2
Dividing both sides by 0.967 atm:
(1065 L * K * 303.15 K) / (275.15 K * 0.967) = V2
Calculating the expression on the left side:
103762.53 L*K = V2
Therefore, the new volume of the balloon in Columbus is approximately 103762.53 L*K.