SOLUTION: The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V=253.5 in^3 when T=390 degrees a

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Question 977574: The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2. What is the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2?
Found 2 solutions by Cromlix, Edwin McCravy:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P.
V = kT/P
To find k use values given.
253.5 = k390/20
k = (253.5 x 20)/390
k = 13
Formula now:-
V = 13T/P
V = (13 x 400)/10
Volume = 520 in^3
Hope this helps:-)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1. Write k equation.
2. Substitute set of given values of all variables.
3. Solve for k
4. Substitute k in k equation.
5. Substitute set of all but one given variable.
6. Solve for the value of the missing variable.

1.
V%22%22=%22%22k%2Aexpr%28T%2FP%29

A measuring device is calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2.
2.
253.5%22%22=%22%22k%2Aexpr%28390%2F20%29

3.
253.5%22%22=%22%22k%2Aexpr%2839%2F2%29

Multiply both sides by 2

507%22%22=%22%2239k

13%22%22=%22%22k

4.
V%22%22=%22%22k%2Aexpr%28T%2FP%29

V%22%22=%22%2213%2Aexpr%28T%2FP%29

What is the volume on this device when the temperature
is 400 degrees and the pressure is 10 lb/in^2
5.
V%22%22=%22%2213%2Aexpr%28400%2F10%29

6.
V%22%22=%22%22520in³

Edwin