   Chapter 10, Problem 13PS

Chapter
Section
Textbook Problem

One of the cylinders of an automobile engine has a volume of 400. cm3. The engine takes in air at a pressure of 1.00 atm and a temperature of 15 °C and compresses the air to a volume of 50.0 cm3 at 77 °C. What is the final pressure of the gas in the cylinder? (The ratio of before and after volumes—in this case, 400:50 or 8:1—is called the compression ratio.)

Interpretation Introduction

Interpretation:

Given the initial volume, temperature and pressure of a gas and the pressure of the gas at new volume 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=1atmP2=?T1=17°C=290KT2=77°C=350KV1=400cm3V

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