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:3.9

Explanation:

Answer 2

Answer:

$\large \boxed{\text{3.9 L}}$

Explanation:

We can use the Combined Gas Laws to solve this problem

$\dfrac{p_{1}V_{1} }{T_{1}} = \dfrac{p_{2}V_{2}}{T_{2}}$

Data

p₁ = 571.2 Torr;  p₂ = 400 Torr

V₁ = 3.5 L;          V₂ = ?

T₁ = 21.5 °C;        T₂ = 6.8 °C

Calculations

(a) Convert the temperatures to kelvins

T₁ = (21.55 + 273.15) K = 294.70 K

T₂ =   (6.8  + 273.15) K = 279.95  K

(b) Calculate the new volume

$\begin{array}{rcl}\dfrac{p_{1}V_{1} }{T_{1}} & = & \dfrac{p_{2}V_{2}}{T_{2}}\\\\\dfrac{\text{571.2 Torr \times 3.5 L}}{\text{294.65 K}} & = & \dfrac{\text{400 Torr} \times V_{2}}{\text{279.95 K}}\\\\\text{6.78 L} & = & \text{1.429V}_{2}\\\\V_{2} & = & \textbf{4.7 L}\\\end{array}\\\text{The new volume of the balloon is \large \boxed{\textbf{4.7 L}} }$