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Chapter 3: Q18-3E (page 610)

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m3. If the temperature remains constant, what is the final value of the pressure?

Short Answer

Expert verified

The final value of the pressure is 0.10012 atm

Step by step solution

01

Boyle’s law

As per Boyle鈥檚 law, the pressure variation with volume is inversely proportional to each other at a constant temperature and is expressed as

P鈭�1V

It can be written as

PV=constant

This can be written as a relationship between two separate cases:

P1V1=P2V2

Here, P1鈥刟苍诲鈥�V1are the initial values of pressure and volume, and P2鈥刟苍诲鈥�V2are the final values. The expression for the final pressure is thus written as

P2=P1V1V2 鈥︹赌︹赌�.(1)
02

Given data

  • The initial pressure isP1=0.355鈥刟迟尘
  • The initial volume is role="math" localid="1655806949022" V1=0.110m3
  • The final volume is role="math" localid="1655806962923" V2=0.390m3
03

Calculation of the final value of the pressure

Putting the values in Equation (1), we get

P2=0.355脳0.1100.390P2=0.10012鈥刟迟尘

Thus, the final value of the pressure is 0.10012 atm

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