Example 1
The pressure and temperature inside an insulated hot-beverage bottle is related to the volume of the bottle and the amount of beverage in it by a real-world form of the ideal gas law. The ideal gas law is given by the formula , in which is the number of moles (a unit of counting) of the gas in a container, is the pressure the gas exerts on the container, is the volume of the container, and is the temperature in degrees Kelvin. The only constant in the formula is . Rearrange the formula to show how the temperature is affected by doubling each variable , , and . (Note: All of the quantities in the formula are nonzero.)
- Isolate temperature, , in the given formula, .
- Determine how is affected in the rearranged formula if is doubled and and stay the same.
- Determine how is affected in the rearranged formula if is doubled and and stay the same.
- Determine how is affected in the rearranged formula if is doubled and and stay the same.