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

May 16, 2016

The final temperature is 133 °C.

#### Explanation:

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)|)

${P}_{1} = {\text{14.7 lb/in}}^{2}$; ${T}_{1} = \text{-15.0 °C" = "258.15 K}$
${P}_{2} = {\text{23.1 lb/in}}^{2}$; ${T}_{2} = \text{?}$
T_2=T_1 × P_2/P_1
${T}_{2} = \text{258.15 K" × (23.1 color(red)(cancel(color(black)("lb/in"^2))))/(14.7 color(red)(cancel(color(black)("lb/in"^2)))) = "405.7 K" = "133 °C}$