Question

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)?

Answer 1

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

Explanation:

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

`color(blue)(bar(ul(|color(white)(a/a)(p_1V_1)/T_1 = (p_2V_2)/T_2color(white)(a/a)|)))" "`

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"`