A sealed gas cylinder on the back of an open truck experiences a temperature change from -19.0 °C to 37.9 °C as it is driven from North Dakota to Arizona. If the pressure gauge on the tank reads 131.4 atm in North Dakota, what will the gauge read in Arizona, in atm?

Note: Do not use scientific notation or units in your response. Enter your response to four decimal places.

To determine the pressure gauge reading in Arizona, we can apply the ideal gas law, assuming that the volume of the gas and the amount of gas molecules remain constant. The law can be simplified to Charles's Law for this scenario, where the pressure of a gas is directly proportional to its absolute temperature when volume and number of moles are held constant. The formula used is

P1/T1 = P2/T2, where
P1 is the initial pressure,
T1 is the initial temperature in Kelvins,
P2 is the final pressure and
T2 is the final temperature in Kelvins.

First, convert the Celsius temperatures to Kelvins: T1 = -19.0 °C + 273.15

= 254.15 K and T2

= 37.9 °C + 273.15

= 311.05 K. Then, solve for P2 using the formula P2 = (P1 * T2) / T1. Plug in the values:

P2 = (131.4 atm * 311.05 K) / 254.15 K.

Performing the calculation gives us P2 = 163.4486 atm. Therefore, the pressure gauge in Arizona will read 163.4486 atm.