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Chapter 8: Problem 145

A certain flexible weather balloon contains helium gas at a volume of \(855\) \(\mathrm{L}\). Initially, the balloon is at sea level where the temperature is \(25^{\circ} \mathrm{C}\) and the barometric pressure is \(730\) torr. The balloon then rises to an altitude of \(6000 \mathrm{ft}\), where the pressure is \(605\) torr and the temperature is \(15^{\circ} \mathrm{C}\). What is the change in volume of the balloon as it ascends from sea level to \(6000 \mathrm{ft} ?\)

Short Answer

Expert verified
The change in volume of the weather balloon as it ascends from sea level to 6000 ft is approximately \(112.74 \mathrm{L}\).

Step by step solution

01

Convert temperatures to Kelvin

To work with the ideal gas law, we need the temperatures in Kelvin. Convert the given temperatures from Celsius to Kelvin using the following formula: \[T(K) = T(^\circ\mathrm{C}) + 273.15\]
02

Convert pressure units

Pressure units should be consistent. In this case, both initial and final pressures are given in torr. It is not necessary to convert them to other units.
03

Apply the ideal gas law for the initial state

At sea level (initial state) where the temperature is \(25^\circ\mathrm{C}\) and the pressure is 730 torr, apply the ideal gas law to find the value of the constant k for the helium gas. \[P_1V_1 = k(T_1)\]
04

Apply the ideal gas law for the final state

At an altitude of 6000 ft (final state) where the temperature is \(15^\circ\mathrm{C}\) and the pressure is 605 torr, apply the ideal gas law again to find the value of the constant k for the helium gas. \[P_2V_2 = k(T_2)\]
05

Find the final volume

Since the values of the constant k found in both equations (initial and final states) are equal, we can equate the right sides of equations from Step 3 and Step 4, and solve for the final volume, \(V_2\).
06

Find the change in volume

The change in volume of the balloon can be found by subtracting the initial volume from the final volume. This will give us the overall change in volume as the balloon rises from sea level to 6000 ft.

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Most popular questions from this chapter

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