   Chapter 10, Problem 14PS

Chapter
Section
Textbook Problem

A helium-filled balloon of the type used in long-distance flying contains 420,000 ft3 (1.2 × 107 L) of helium. Suppose you fill the balloon with helium on the ground, where the pressure is 737 mm Hg and the temperature is 16.0 °C. When the balloon ascends to a height of 2 miles, where the pressure is only 600. mm Hg and the temperature is ‒33 °C, what volume is occupied by the helium gas? Assume the pressure inside the balloon matches the external pressure.

Interpretation Introduction

Interpretation:

Given the initial volume, temperature and pressure of a helium gas and the volume of the gas at new pressure and temperature has to be given.

Concept Introduction:

Different laws have been put forward to introduce properties of gases:

Boyle’s law:

At fixed temperature, the volume of a fixed amount of gas is inversely proportional to the pressure exerted by the gas.

P1V(n,Twillbeconstant)

Charles’s law: States that volume is directly proportional to temperature when the gas is held

at constant pressure and number of molecules.

VT

General Gas Law: Combining Charles’s law and Boyle’s law we get the General gas law or combined gas law.

P1V1T1=P2V2T2

Explanation

From Combined Gas law,

P1V1T1=P2V2T2

Given data:

P1=737mmHgP2=600mmHgT1=16°C=289KT2=-33°C=240KV1=1

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