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6. The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to
the temperature of the gas. If the pressure is 6 pounds per square inch when the temperature is 440° F,find
the pressure exerted when the temperature of the gas is 380°F.
(SHOW WORK)

Answer :

JeanaShupp

Answer: 5.18 pounds

Step-by-step explanation:

Given: The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to  the temperature of the gas.

Let 'p' denote the pressure exerted on the walls and 't' denotes  temperature of the gas.

Then the equation is given by :-

[tex]p=ct[/tex], where c is the proportionality constant.

Also, the pressure is 6 pounds per square inch when the temperature is 440° F.

[tex]\Rightarrow\ 6=440c\\\\\Rightarrow\ c=\dfrac{6}{440}=\dfrac{3}{220}[/tex]

Then, the final equation to calculate pressure becomes :-

[tex]p=\dfrac{3}{220}t[/tex]

Now, the pressure exerted when the temperature of the gas is 380°F is given by :-

[tex]p=\dfrac{3}{220}\times380=5.181818\approx5.18\text{ pounds}[/tex]

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