A gas filled balloon having a volume of 3.0 L at 1.1 atmosphere of pressure and a temperature of 22 C is allowed to rise into the stratosphere where the temperature and pressure are: - 28 C (note the negative sign) and 0.002 atmospheres , respectively. What is the approximate final volume of the balloon in liters (L) when it reaches this level in the atmosphere
1302L
To find the final volume of the balloon in liters when it reaches the given level in the atmosphere, we can use the combined gas law. The combined gas law is expressed as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where:
P1 = initial pressure (in atmospheres)
V1 = initial volume (in liters)
T1 = initial temperature (in Kelvin) - Remember to convert Celsius to Kelvin using the formula K = °C + 273.15
P2 = final pressure (in atmospheres)
V2 = final volume (in liters)
T2 = final temperature (in Kelvin)
Let's solve for V2:
First, let's convert the initial temperature from Celsius to Kelvin.
T1 = 22°C + 273.15 = 295.15 K
Now, we can plug in the values into the combined gas law equation:
(1.1 atm * 3.0 L) / (295.15 K) = (0.002 atm * V2) / (245.15 K)
Cross-multiplying and rearranging the equation, we get:
(1.1 atm * 3.0 L * 245.15 K) = (0.002 atm * V2 * 295.15 K)
Simplifying further:
V2 = (1.1 atm * 3.0 L * 245.15 K) / (0.002 atm * 295.15 K)
V2 ≈ 27.7 L
Therefore, the approximate final volume of the balloon when it reaches the given level in the atmosphere is 27.7 liters (L).