SOLUTION: The volume of gas varies directly as its temperature and inversely as its pressure. At a temperature of 100 kelvin and a pressure of 15 kilograms per square meter, the gas occupies

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Question 673759: The volume of gas varies directly as its temperature and inversely as its pressure. At a temperature of 100 kelvin and a pressure of 15 kilograms per square meter, the gas occupies a volume of 20 cubic meters. Find the volume at a temperature of 150 kelvin and a pressure of 20 kilograms per square meter.
Found 2 solutions by vleith, Theo:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
volume+=+k+%2A%28temperature%2FPressure%29
Plug in the value given as the first part of the problem.
Then solve to find k
20+=+k+%2A%28100%2F15%29+
20+%2A+15%2F100+=+k
3+=+k
so
volume+=+3+%2A+%28temperature%2Fpressure%29
Use that to solve for the second volume
volume+=+3+%2A+%28150%2F20%29
volume+=+22.5 cubic meters

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
direct proportion is z = kx
inverse proportion is z = k/y
direct and inverse proportion together is z = kx/y
z = volume of gas in cubic meters
x = temperature in kelvin
y = pressure in kilograms per square meter.
when volume of gas is 20 cubic meters and temperature is 100 kelvin and pressure is 15 kilograms per square meter, equation of z = kx/y becomes 20 = 100k/15.
solve for k to get k = 20*15/100 which results in k = 3.
now that you know k, you can use that to solve the problem.
when the temperature is 150 kelvin and the pressure is 20 kilograms per square and k = 3, the equation of z = kx/y becomes z = 3*150/20 which becomes z = 22.5 cubic meters.
that's your answer.