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(39621)   (Show Source): You can put this solution on YOUR website!
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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.

Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
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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