# A weather balloon has a volume of (7.20x10^1) L when at the surface where the pressure is (9.3000x10^1) kPa and a temperature is (2.6000x10^2) K. (see more below)?

May 3, 2017

The pressure is 3.35 × 10^1color(white)(l) "kPa".

#### Explanation:

This looks like a case where we can use the combined gas laws:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \frac{{p}_{1} {V}_{1}}{T} _ 1 = \frac{{p}_{2} {V}_{2}}{T} _ 2 \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this formula to get

p_2 = p_1 × V_1/V_2 × T_2/T_1

In this problem,

p_1 = 9.3000 × 10^1 color(white)(l)"kPa"; V_1 = 7.20 × 10^1color(white)(l) "L"; color(white)(m)T_1 = 2.6000 × 10^2 color(white)(l)"K"
p_2 = ?;color(white)(mmmmmmmll) V_2 = 1.0000 × 10^2color(white)(l) "L"; T_2 = 1.3000 × 10^2color(white)(l) "K"

p_2 = 9.3000 × 10^1 color(white)(l)"kPa" × (7.20 × 10^1 color(red)(cancel(color(black)("L"))))/(1.0000 × 10^2 color(red)(cancel(color(black)("L")))) × (1.3000 × 10^2 color(red)(cancel(color(black)("K"))))/(2.6000 × 10^2 color(red)(cancel(color(black)("K"))))

= 3.35 × 10^1color(white)(l) "kPa"