Question

Question #8fca6

Answer 1

`"1090 K"`

Explanation:

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

`color(blue)(ul(color(black)((P_1V_1)/T_1 = (P_2V_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 = "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 * P_1" "` and `" "V_2 = 2 * V_1`

Rearrange the combined gas law equation to solve for `T_2`

`(P_1V_1)/T_1 = (P_2V_2)/T_2 implies T_2 = P_2/P_1 * V_2/V_1 * 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.