A motorist fills his car tires to 32 lb/in2 pressure at a temperature of 30°C. Assuming no change in volume,
what will the pressure in the tires be when the motorist drives across Death Valley, with a pavement temperature of 78°C?
A. 37 lb/in 2 B. 83 lb/in 2 C. 12 lb/in 2 D. 4.8 lb/in 2 E. 28 lb/in2
We're dealing with a gas here, so keeping the Ideal Gas Law
pV = nRT
in mind, is a good idea
Since we're not interested in the type of gas, i.e. moles (so we don't need R either)
and the volume remains constant,
pV = nRT
we'll end up with
p = T, also called Gay-Lussac's Law
Now, we can set up a ratio
32 lb/in2/x
=
30°C/78°C
to make this a bit easier and cleaner, let's flip the equation
x/32 lb/in2
=
78°C/30°C
x =
[(32 lb/in2)(78°C)]/30°C
x = 83.2 lb/in2
The pressure in the tires will be 83 lb/in2 Answer B is the correct option