Question

determining the volume of a weather balloon
a weather balloon is filled to a volume of 6000 l while it is on the ground, at a pressure of 1 atm and a temperature of 273 k. the balloon is then released into the atmosphere. as the balloon rises, the pressure decreases to 0.3 atm and the temperature decreases to 240 k. what is the final volume of the balloon at this temperature and pressure? round your answer to the nearest tenth.
l

Explanation:

Step1: Identify the combined - gas law formula

The combined - gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$.

Step2: Identify the given values

$P_1 = 1\ atm$, $V_1=6000\ L$, $T_1 = 273\ K$, $P_2 = 0.3\ atm$, $T_2=240\ K$.

Step3: Rearrange the formula to solve for $V_2$

$V_2=\frac{P_1V_1T_2}{T_1P_2}$.

Step4: Substitute the values into the formula

$V_2=\frac{1\times6000\times240}{273\times0.3}$.
First, calculate the numerator: $1\times6000\times240 = 1440000$.
Then, calculate the denominator: $273\times0.3=81.9$.
Now, divide: $V_2=\frac{1440000}{81.9}\approx17582.4$.

Answer:

$17582.4$