SOLUTION: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. A cylinder contains oxygen at a temperature of 310 degrees K and a pressure o
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Question 1137495: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. A cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. What is the pressure if the volume is decreased to 100 liters and the temperature is increased to 320 degrees K? Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39620) (Show Source):
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The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P.
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-------using lower-case k as the variation constant
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cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters.
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What is the pressure if the volume is decreased to 100 liters and the temperature is increased to 320 degrees K?
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This questions asks for P, given certain values of V and T.
From the condition, you have this general formula
V = ,
where " k " is a constant value.
From the condition, you also have these two expressions for two states of the gas:
120 = (1)
and
100 = , (2)
where P is the unknown pressure under the question.
Divide expression (1) by expression (2) (both sides). You will get
= , or
1.2 = .
which implies
P = = 22.297 atmospheres. ANSWER
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It is the shortest way to solve such problems.
The other approach with calculating the constant value " k " forces you to make unnecessary calculations on the way to the answer.
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