Answer :
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;
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