SOLUTION: The pressure P of a gas varies directly as the temperature T and inversely as the volume V. When T=50 and V=275 cubic inches, P = 20 lb/min . FIND THE PRESSURE of a gas when T=60 a

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Question 1097283: The pressure P of a gas varies directly as the temperature T and inversely as the volume V. When T=50 and V=275 cubic inches, P = 20 lb/min . FIND THE PRESSURE of a gas when T=60 and V = 250 cubic inches. [Make the answer very clear]
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE FIFTH-GRADER APPROACH:
Pressure P varies directly as the temperature T,
so as the temperature increases multiplied by a factor of 60%2F50 ,
the pressure should be multiplied by the same factor.
Pressure P varies inversely with volume V,
so as the volume decreases from 275 to 250,
the pressure should increase by the corresponding ratio,
multiplied by the factor 275%2F250 .
The change in T makes P increase, and so does the change in V.
So, the final pressure is the initial one times those greater than 1 factors:
P=20%2A%2860%2F50%29%2A%28275%2F250%29=26.4
THE WAY I HAVE SEEN IT TAUGHT IN HIGH SCHOOL:
Step 1:
Find an equation/formula that relates P ,T and V .
P varies directly with T means P=something%2AT ,
where that something does not depend on T .
P varies inversely with V means P=factor%2A%281%2FV%29 ,
where that factor does not depend on V .
The problem question does not say so,
but you are expected to assume that P depends on T and V and nothing else.
I assume that too, because it is what I was taught in high school through college.
If P does not depend on anything else,
P=k%2AT%2A%281%2FV%29 <--> P=kT%2FV ,
where k is a constant that does not depend on anything else.

Step 2:
Use the data supplied to find k .
[NOTE: The units "lb/min" are not units I have ever seen used for anything, and they certainly could not represent pressure. Maybe that is a typo. The usual units for pressure are lb/square inch, although bars, atmospheres, Pascals, millimiters of mercury, inches of mercury, and inchres of water are also used.]
As we are going to be using the same units for P, T and V, we can leave them out of the equation.
Substituting the data for the situation that we know everything about,
system%28P=20%2CT=50%2CV=275%29 into P=kT%2FV ,
we get 20=k%2A50%2F275 --> 20%2A%28275%2F50%29=%28k%2A50%2F275%29%2A%28275%2F50%29 --> 20%2A550%2F50=k%2Across%2850%29%2Across%28275%29%2F%28cross%28275%29%2Across%2850%29%29 --> 110=k

Step 3:
Use the equation/formula found and the k value found to calculate the missing meassurement in system%28P=%22%3F%22%2CT=60%2CV=250%29 .
P=110%2A60%2F250=6600%2F250=26.4 .
NOTE: You will have to decide if you need to show the pressure units in your answer, and what units to show.