# Question 8fca6

Jan 31, 2017

$\text{1090 K}$

#### Explanation:

Your tool of choice here will be the combined gas law equation, which looks like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2}}}$

Here

• ${P}_{1}$, ${V}_{1}$, ${T}_{1}$ are the pressure, volume, and absolute temperature of the gas at an initial state
• ${P}_{2}$, ${V}_{2}$, ${T}_{2}$ are the pressure, volume, and absolute temperature of the gas at a final state

In your case, you know that

${T}_{1} = \text{273 K}$

and that the pressure and volume of the gas must double as a result of the increase in temperature. You can say that

${P}_{2} = 2 \cdot {P}_{1} \text{ }$ and $\text{ } {V}_{2} = 2 \cdot {V}_{1}$

Rearrange the combined gas law equation to solve for ${T}_{2}$

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2 \implies {T}_{2} = {P}_{2} / {P}_{1} \cdot {V}_{2} / {V}_{1} \cdot {T}_{1}$

Plug in your values to find

T_2 = (2 * color(red)(cancel(color(black)(P_1))))/color(red)(cancel(color(black)(P_1))) * (2 * color(red)(cancel(color(black)(V_1))))/color(red)(cancel(color(black)(V_1))) * "273 K" = color(darkgreen)(ul(color(black)("1090 K")))#

The answer is rounded to three sig figs.