Question

When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 114 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 57 cubic inches. A) 26 pounds per square inch B) 14 pounds per square inch C) 28 pounds per square inch 57 D) pounds per square inch 14

Answer 1

Let V represents the volume of the gas

Let P represents the pressure of the gas

Let T represents the temperature which is a constant

`\begin{gathered} \text{ Volume is inversely proportional to pressure, this is represented as} \\ \text{ V }\propto\text{ }(1)/(P) \\ \text{ Introducing constant T},\text{ we have} \\ \text{ V = }(T)/(P)----------law \\ \text{ When }V=114in^3,\text{ P= 14 lb} \\ \text{ substituting these values of V and P into the law, we have} \\ 114=(T)/(14) \\ T=114\text{ x 14} \\ T=1596 \\ \text{The law becomes} \\ \text{ V=}(1596)/(P) \end{gathered}`

When the volume is decreased to 57 cubic inches, we will have to substitute V=57 into the law and obtain the value of P

`\begin{gathered} \text{ V=}(1596)/(P) \\ \\ 57\text{ =}(1596)/(P) \\ 57P=1596 \\ P=(1596)/(57) \\ P=28\text{ } \\ \\ \text{Hence , the new pressure is 28 pounds per square inch} \end{gathered}`

The correct option is option C