Mechanical Engineering Principles

260 MECHANICAL ENGINEERING PRINCIPLES

Hence

V 1

423

=

2

3

V 1

T 2

from which,final temperature,

T 2 =^23 ( 423 )=282 Kor( 282 − 273 )°C i.e. 9 °C

Now try the following exercise

Exercise 120 Further problems on Char-

les’ law

1. Some gas initially at 16°C is heated to
   96 °C at constant pressure. If the initial
   volume of the gas is 0.8 m^3 , determine
   the final volume of the gas. [1.02 m^3 ]


2. A gas is contained in a vessel of volume
   0.02 m^3 at a pressure of 300 kPa and a
   temperature of 15°C. The gas is passed
   into a vessel of volume 0.015 m^3. Deter-
   mine to what temperature the gas must
   be cooled for the pressure to remain the
   same. [− 57 °C]


3. In an isobaric process gas at a temperature
   of 120°C has its volume reduced by a
   sixth. Determine the final temperature of
   the gas. [54.5°C]

23.4 The pressure law

Thepressure lawstates:

the pressure p of a fixed mass of gas is directly propor-

tional to its thermodynamic temperature T at constant

volume.

i.e. p∝Torp=kTor

p

T

=k

When a fixed mass of gas at constant volume
changes from pressurep 1 and temperatureT 1 ,to
pressurep 2 and temperatureT 2 then:

p 1

T 1

=

p 2

T 2

Problem 6. Gas initially at a temperature of

17 °C and pressure 150 kPa is heated at

constant volume until its temperature is

124 °C. Determine the final pressure of the

gas, assuming no loss of gas.

Since the gas is at constant volume, the pressure law

applies, i.e.

p 1

T 1

=

p 2

T 2

whereT 1 =( 17 + 273 )K=

290 K,T 2 =( 124 + 273 )K=397 K and

p 1 =150 kPa.

Hence,

150

290

=

p 2

397

from which,final pressure,

p 2 =

( 150 )( 397 )

290

= 205 .3kPa

Now try the following exercise

Exercise 121 A further problem on the

pressure law

1. Gas, initially at a temperature of 27°Cand
   pressure 100 kPa, is heated at constant
   volume until its temperature is 150°C.
   Assuming no loss of gas, determine the
   final pressure of the gas. [141 kPa]

23.5 Dalton’s law of partial pressure

Dalton’s law of partial pressurestates:

the total pressure of a mixture of gases occupying a

given volume is equal to the sum of the pressures of

each gas, considered separately, at constant tempera-

ture.

The pressure of each constituent gas when occupy-

ing a fixed volume alone is known as thepartial

pressureof that gas.

An ideal gasis one that completely obeys the

gas laws given in Sections 23.2 to 23.5. In practice

no gas is an ideal gas, although air is very close to

being one. For calculation purposes the difference

between an ideal and an actual gas is very small.

Problem 7. A gasRin a container exerts a

pressure of 200 kPa at a temperature of

18 °C. GasQis added to the container and

the pressure increases to 320 kPa at the same

temperature. Determine the pressure that gas

Qalone exerts at the same temperature.