A balloon with a volume of 5.3 L is taken from an indoor temperature of 24 C to the outdoors. The volume of the balloon outside is 4.9 L. How do you determine the C temperature outside?

Md Ariful Islam

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Md Ariful Islam

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Given

The volume $V_1$ of a gas at a temperature $T_1$.
A second volume $V_2$

Find

The second temperature $T_2$

Strategy

A problem involving two gas volumes and two temperatures must be a problem.

The formula for is

$color(blue)(|bar(ul(color(white)(a/a) V_1/T_1 = V_2/T_2color(white)(a/a)|)))" "$

Solution

We can rearrange Charles' Law to get

$T_2 = T_1 × V_2/V_1$

In your problem,

$V_1 = "5.3 L"$; $T_1 = (24 + 273.15) K = "297.15 K"$
$V_2 = "4.9 L"$; $T_2 = "?"$

∴ $T_2 = "297.15 K" × (4.9 cancel("L"))/(5.3 cancel("L")) = "274 K"$

$"200 K" = "(274 - 273.15) °C" = "0 °C"$

The outside temperature is 0 °C.

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