Question #8fca6

1 Answer
Jan 31, 2017

Answer:

#"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.