Consider a balloon that has a volume V. It contains n moles of gas, it has an internal pressure of P, and its temperature is T. If the balloon is heated to a temperature of 15.5T while it is placed under a high pressure of 15.5P, how does the volume of the balloon change?

For a fixed amount of gas, the ideal gas law gives V = nRT/P, so volume is proportional to temperature divided by pressure. Both temperature and pressure are multiplied by 15.5, so their ratio is unchanged: (15.5T)/(15.5P) = T/P. Therefore, the balloon’s volume stays the same.

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