A balloon is filled with helium gas at 23 degrees C. The balloon expands until the pressure is equal to the atmospheric pressure of 755 toor. The balloon rises to an altitude of 6000 feet where the pressure is 550 toor and the temperature is 5 degrees C. Calculate the percent increase in volume of the balloon as it ascends to 6000 feet?
Use (P1V1/T1) = P2V2/T2) and calculate the new volume at 6000 ft.
Then [(V2-V1)/V1]*100 = ??
To calculate the percent increase in volume of the balloon as it ascends to 6000 feet, we need to use the ideal gas law:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
In this case, we will assume that the number of moles and the gas constant remain constant.
Let's start by finding the initial volume of the balloon at 23 degrees C and 755 toor. We'll call this volume V1.
Using the ideal gas law equation:
V1 = nRT1 / P1
Now, let's find the final volume of the balloon at 5 degrees C and 550 toor. We'll call this volume V2.
V2 = nRT2 / P2
To calculate the percent increase in volume, we'll use the formula:
Percent increase = ((V2 - V1) / V1) * 100
Now, let's plug in the values and calculate the percent increase.
Step 1: Convert temperature from degrees Celsius to Kelvin.
T1 = 23 + 273 = 296 K
T2 = 5 + 273 = 278 K
Step 2: Calculate the initial volume of the balloon (V1).
V1 = nRT1 / P1
Step 3: Calculate the final volume of the balloon (V2).
V2 = nRT2 / P2
Step 4: Calculate the percent increase in volume.
Percent increase = ((V2 - V1) / V1) * 100
Follow the above steps, plug in the values, and perform the calculations to find the percent increase in volume of the balloon as it ascends to 6000 feet.