Question

A certain flexible weather balloon contains 3.5 L of helium gas. Initially, the balloon is in WP at 8500ft, where the temperature is 21.5C and the barometric pressure is 571.2 torr. The balloon then is taken to the top of Pike's Peak at an altitude of 14,100ft, where the pressure is 400 torr and the temperature is 6.8C. What is the new volume of the balloon at the top of Pikes Peak?

Answer 1

Answer:

4.75 mL is the new volume of the balloon at the top of Pikes Peak.

Explanation:

The combined gas equation is,

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where:

$P_1$ = initial pressure of helium gas , at 8500 feet = 571.2 Torr

$V_1$ = initial volume of helium gas , at 8500 feet= $3.5 L$

$T_1$ = initial temperature of helium gas , at 8500 feet= $21.5^oC=273+21.5=294.5 K$

$P_2$ = final pressure of helium gas, at 14,100 feet = 400 Torr

$V_2$ = final volume of helium gas, at 14,100 feet = ?

$T_2$ = final temperature of helium gas , at 14,100 feet= $6.8^oC=273+6.8=279.8 K$

Now put all the given values in the above equation, we get:

$\frac{571.2 Torr\times 3.5 L}{294.5 K}=\frac{400 Torr\times V_2}{279.8 K}$

$V_2=\frac{571.2 Torr\times 3.5 L\times 279.8 K}{294.5 K\times 400 Torr}$

$V_2=4.75 mL$

4.75 mL is the new volume of the balloon at the top of Pikes Peak.