Answer :
Final answer:
The final pressure in the refrigeration system, assuming no nitrogen escaped, would be 94.3 psig.
Explanation:
To solve this problem, we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since the volume is constant, we can rewrite the equation as P1/T1 = P2/T2.
Given that the initial pressure, P1, is 100 psig (psig means pounds per square inch gauge) and the temperature, T1, is 75 degrees Fahrenheit (which is 297.039 Kelvin), we can plug these values into the equation. The final temperature, T2, is 50 degrees Fahrenheit (which is 283.15 Kelvin). Rearranging the equation to solve for P2, we have P2 = P1 * T2/T1. Plugging in the values, we get:
P2 = 100 psig * 283.15 K / 297.039 K = 94.3 psig
