The pressure on one cubic foot of air at -15.0°C was increased from $14.7$ $lb$ $/$ $i$ $nch^2$ squared to 23.1 $lb$ $/$ $i$ $nch^2$ . What is the final temperature, in °C, if the volume remained constant?

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Answer 1 · 2016-05-16T21:50:56

The final temperature is 133 °C.

Since the volume is constant, this is an example of a problem involving Gay-Lussac's Law:

$color(blue)(|bar(ul(P_1/T_1=P_2/T_2)|)$

Your data are:

$P_1 = "14.7 lb/in"^2$ ; $T_1 = "-15.0 °C" = "258.15 K"$
$P_2 = "23.1 lb/in"^2$ ; $T_2 = "?"$

We can rearrange the above formula to get

$T_2=T_1 × P_2/P_1$

$T_2 = "258.15 K" × (23.1 color(red)(cancel(color(black)("lb/in"^2))))/(14.7 color(red)(cancel(color(black)("lb/in"^2)))) = "405.7 K" = "133 °C"$

The pressure on one cubic foot of air at -15.0°C was increased from 14.714.7 lblb//iinch^2nch^2 squared to 23.1 lblb//iinch^2nch^2. What is the final temperature, in °C, if the volume remained constant?