Part A

All pressure$-$volume$-$temperature relationships for gases can be combined into a single relationship known as the combined gas law. This expression can be used when looking at the effect of changes in two of these variables on the third as long as the amount of gas $($number of moles$)$ remains constant. To use the combined gas law properly, you must always express the temperatures in kelvins. The combined gas law can be represented as follows:

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

A very flexible helium$-$filled balloon is released from the ground into the air at $20.C.$ The initial volume of the balloon is $5\mathrm{.}00L,$ and the pressure is $760.mmHg.$ The balloon ascends to an altitude of $20km,$ where the pressure is $76\mathrm{.}0mmHg$ and the temperature is $-50.C.$ What is the new volume, $V_2,$ of the balloon in liters, assuming it doesn't break or leak?

Express your answer numerically in liters.

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$[$:$V_2=\}$