SOLUTION: Another Inverse and Joint Variation question. Chemistry Gas Laws. The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. Write an

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Question 161607This question is from textbook College Algebra
: Another Inverse and Joint Variation question.
Chemistry Gas Laws. The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. Write an equation relating V,T, and P using k as the constant of proportionality. If a cylinder contains oxygen at a temperature of 300 K and a pressure of 15 atmospheres in a volume of 100 liters, what is the constant of proportionality k? If a pistion is lowered into the cylinder, decreasing the volume occupied by the gas to 80 liters and raising the temperature to 310 K, what is the gas pressure. This question is from textbook College Algebra

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The volume V of an ideal gas varies directly with the temperature T & inversely
with the pressure P. Write an equation relating V,T, and P using k as the
constant of proportionality. If a cylinder contains oxygen at a temperature of
300 K and a pressure of 15 atmospheres in a volume of 100 liters, what is the
constant of proportionality k?
The equation for this:
V =
Where:
V = 100
T = 300
P = 15
:
= 100
Multiply both sides by 15, results:
300k = 15(100)
k =
k = 5
:
V = is the formula
:
:
If a piston is lowered into the cylinder, decreasing the volume occupied by
the gas to 80 liters and raising the temperature to 310 K, what is the gas
pressure
:
In the above equation:
V = 80
T = 310
find P
:
80 =
Multiply both sides by P
80P = 1550
P =
P = 19.375 atmospheres