# A balloon is filled with 14 L of gas at 302 K. What is its temperature in Kelvin when the volume expands to 20 L, assuming pressure remains constant?

##### 1 Answer

#### Explanation:

The thing to remember about *volume* and *temperature* is that they have a **direct relationship** when pressure and number of moles of gas * remain constant*.

This relationship is known as **Charles' Law** and states that when those conditions are met, **increasing** the temperature of the gas will result in an **increase** in volume.

Similarly, **decreasing** the temperature of the gas will result in a **decrease** in volume.

Mathematically, this is expressed as

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

In your case, the volume **expanded** from an initial value of **increased** as well, i.e.

Rearrange the above equation to solve for

#V_1/T_1 = V_2/T_2 implies T_2 = V_2/V_1 * T_1#

Plug in your values to find

#T_2 = (20 color(red)(cancel(color(black)("L"))))/(14color(red)(cancel(color(black)("L")))) * "302 K" = "431.43 K"#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one sig fig for the final volume of the gas

#T_2 = color(green)(|bar(ul(color(white)(a/a)color(black)("430 K")color(white)(a/a)|)))#