Middle School

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A gas is compressed inside a compressor's cylinder. When the piston is at its bottom dead center, the gas is initially at 10 psig, 65 degrees Fahrenheit, and 10 cubic inches. After compression and when the piston is at top dead center, the gas is 180 degrees Fahrenheit and occupies 1.5 cubic inches. What would be the new pressure of the gas in psig?

Answer :

Based on gas laws:

PV/T = Constant, P = Pressure, V = volume, T = Temperature (K)
Therefore,
P1V1/T1 = P2V2/T2

P1 = 10 psig
V1 = 10 in^3
T1 = 65°F = 291.483 K
P2 = ?
V2 = 1.5 in^3
T2 = 180°F = 355.372 K

Rearranging the equation,
P2 = P1V1T2/T1V2 = (10*10*355.372)/(291.483*1.5) = 81.279 psig

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Rewritten by : Barada

Final answer:

Explanation on how to calculate the new pressure of a gas when compressed inside a compressor's cylinder.

Explanation:

A gas is compressed inside a compressor's cylinder. Initially, the gas is at 10 psig, 65 degrees Fahrenheit, and 10 inches cubed.

Given that after compression, at 180 degrees Fahrenheit and occupying 1.5 inches cubed, we can use the ideal gas law:

Final pressure = (initial pressure * initial volume * final temperature) / (final volume * initial temperature)

Final pressure = (10 psig * 10 in³ * 180°F) / (1.5 in³ * 65°F)

Final pressure = 240 psig