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Question 1174192: 10. 4 cubic feet of air at a pressure of 18 pounds per square inch were compressed to a volume of 3 cubic feet. At the same time, the air was heated from an absolute temperature of 288° to one of 308° (from 59° to 95° F). What was its pressure then? (show the solutions with variations thanks!)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
from the internet, i get the following:
volume of a gas is directly proportional to the temperature when the pressure is held constant.
as the temperature goes up, the volume of the gas goes up.
volume of a gas is inversely proportional to the pressure when the temperature is held constant.
as the pressure goes up, the volume of the gas goes down.
your problem states that the volume of the gas is 4 cubic feet when the pressure is 18 pounds per square inch and the temperature is 288 kelvin.
the variation formula would be y = k * x / y
y is the volume of the gas.
x is the temperature
y is the pressure
k is the constant of variation
y = k * x is the direct variation formula.
y = k / y is the inverse variation formula.
when you put them together, you get y = k * x / y
when y = 4 cubic inches, x = 288 kelvin and y = 18 pounds per square inch.
the formula becomes:
4 = k * 288 / 18
solve for k to get:
k = 4 * 18 / 288 = .25
if the volume becomes 3 and the pressure becomes 308, then the formula becomes:
3 = .25 * 308 / y
since k is the constant of variation, it stays the same at .25.
solve for y to get:
y = .25 * 308 / 3 = 25 and 2/3 = 25.67 rounded to 2 decimal places.
that is the pressure when the volume of the gas goes from 4 to 3 and the temperature goes from 288 to 308.
the pressure goes from 18 to 25.67.
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