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9) a) When the temperature stays the same, the volume of a gas varies inversely to the pressure of the gas. Write an equation to express this variation, using k for the constant of variation.

b) When a balloon is filled with 216 cubic inches of a gas the pressure is 14 pounds per square inch. Find the value of the constant of variation, k.
c) Find the pressure of gas if the volume is decreased to 36 cubic inches.

User Syed Saad
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Final answer:

a). The relationship between the pressure and volume of a gas at a constant temperature is represented by the equation PV=k, where P is pressure, V is volume, and k is a constant.

b). Applying this to the given examples, when a balloon is filled with 216 cubic inches of gas at 14 psi, k = 3024.

c). If the volume is reduced to 36 cubic inches, the pressure rises to 84 psi.

Step-by-step explanation:

a). According to the principles of gas laws, when the temperature stays the same, the volume of a gas varies inversely to the pressure of the gas. This can be represented as PV = k where P represents the pressure of the gas, V is the volume of the gas and k is the constant of variation.

b). From the given condition that when the balloon is filled with 216 cubic inches of a gas the pressure is 14 pounds per square inch, we can find the value of the constant of variation by substituting P=14 and V=216 into our equation. so, k = PV = 14 * 216 = 3024.

c). To find the pressure of the gas when the volume is decreased to 36 cubic inches, we would rearrange the equation to solve for P, so P = k / V. This gives us P = 3024 / 36 = 84 pounds per square inch.

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User Tloach
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