Engineering College

A refrigeration system was checked for leaks. The system temperature and surroundings were 75°F when the system was charged with nitrogen to 100 psig. The temperature then dropped to 50°F. What should the pressure be if no nitrogen has escaped?
A) 9 psig
B) 94 psig
C) 100 psig
D) 90 psig

Answers

Answer 1
B 94 psig because the temperature dropped too
Answer 2

The temperature and pressure of an ideal gas are directly proportional

The pressure of the system should be in the range B) 94 psig

The given refrigerator parameters are;

The temperature of the system and the surrounding, T₁ = 75 °F = 237.0389 K

The pressure to which the system was charged with nitrogen, P₁ = 100 psig

The temperature to which the system dropped, T₂ = 50 °F = 283.15 K

The required parameter;

The pressure, P₂, of the system at 50°F

Method:

The relationship between pressure and temperature is given by Gay-Lussac's law as follows;

At constant volume, the pressure of a given mass of gas is directly proportional to its temperature in Kelvin

Mathematically, we have;

[tex]\dfrac{P_1}{T_1} = \mathbf{\dfrac{P_2}{T_2}}[/tex]

Plugging in the values of the variables gives;

[tex]\mathbf{\dfrac{100 \ psig}{297.0389}} = \dfrac{P_2}{283.15}[/tex]

Therefore;

[tex]P_2 = \mathbf{283.15 \, ^{\circ}F \times \dfrac{100 \ psig}{297.0389\ ^{\circ}F} \approx 95.3 \, ^{\circ}F}[/tex]

The closest option to the above pressure is option B) 94 psig

Learn more about Gay-Lussac's law here;

https://brainly.com/question/16302261

A Refrigeration System Was Checked For Leaks. The System Temperature And Surroundings Were 75F When The

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