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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