A gas is compressed inside a compressors cylinder. When the piston is at its bottom dead center , the gas is initially at 10 psig , 65 degree and 10.5 in. After compression and when the piston is at top dead center the gas is 180 degree and occupies 1.5 in. What would be the new pressure of the gas in psig
196.04
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To determine the new pressure of the gas inside the compressor's cylinder, you can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure in absolute units
V = Volume of the gas
n = Number of moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
First, we need to convert the initial and final temperatures from Fahrenheit to Kelvin. The equation for converting Fahrenheit to Kelvin is as follows:
T(K) = (T(°F) + 459.67) × 5/9
Using the given initial temperature of 65 degrees Fahrenheit:
T(initial) = (65 + 459.67) × 5/9
T(initial) ≈ 336.48 Kelvin
Similarly, for the final temperature of 180 degrees Fahrenheit:
T(final) = (180 + 459.67) × 5/9
T(final) ≈ 355.37 Kelvin
Next, we need to convert the initial and final volumes from inches cubed to liters. We know that 1 inch cubed is approximately equal to 16.3871 milliliters or 0.0163871 liters.
Initial volume: V(initial) = 10.5 in³ × 0.0163871 L/in³
V(initial) ≈ 0.172 liters
Final volume: V(final) = 1.5 in³ × 0.0163871 L/in³
V(final) ≈ 0.025 liters
Now, let's substitute the known values into the ideal gas law equation:
P(initial) × V(initial) = P(final) × V(final)
Rearranging the equation to solve for P(final):
P(final) = (P(initial) × V(initial)) / V(final)
Plugging in the values:
P(final) = (10 psig × 0.172 L) / 0.025 L
P(final) ≈ 68.96 psig
Therefore, the new pressure of the gas inside the cylinder after compression would be approximately 68.96 psig.