If a tank were blocked in (all inlets and outlets are closed) late in the evening with a temperature of 62F a pressure gauge attached to it would read an ambient pressure (14.7 PSIA). The next day, as the sun begins to shine directly on the tank, its inside temperature would begin to rise and so would the pressure. If the temperature inside the tank rised to 178F, how much pressure, in PSIG, would now be in the tank?

is this a gas filled tank?

use the combined gas law.

P1V1/T1=P2V2/T2

convert temps to kelvins, pressure PSI if you wish. I prefer to work everything in SI units, like the rest of the world.

Me too!

To calculate the pressure inside the tank, we can use the ideal gas law, which states:

PV = nRT

Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin

Let's assume the volume of the tank is constant, as mentioned in the question. Therefore, we can rewrite the equation as:

P1/T1 = P2/T2

Where:
P1 is the initial pressure (14.7 PSIA)
T1 is the initial temperature (62°F converted to Kelvin)
P2 is the final pressure (which we need to calculate)
T2 is the final temperature (178°F converted to Kelvin)

First, let's convert the temperatures from Fahrenheit to Kelvin using the following formula:

T(°F) + 459.67 = T(K)

Therefore, the initial temperature in Kelvin (T1) is:
T1 = 62°F + 459.67 = 521.67 K

And the final temperature in Kelvin (T2) is:
T2 = 178°F + 459.67 = 637.67 K

Now, we can rearrange the equation to solve for P2:

P2 = (P1 * T2) / T1

Substituting the given values:
P2 = (14.7 PSIA * 637.67 K) / 521.67 K

Calculating the pressure using the formula:
P2 ≈ 17.972 PSIA

However, the question asks for the pressure in PSIG (pound-force per square inch gauge). PSIG is the pressure above atmospheric pressure. To convert from PSIA to PSIG, we subtract the atmospheric pressure, which is 14.7 PSIA in this case.

P2 (PSIG) = P2 (PSIA) - Atmospheric Pressure = 17.972 PSIA - 14.7 PSIA

Therefore, the pressure inside the tank when the temperature rises to 178°F would be approximately 3.272 PSIG.