Page:Text-book of Electrochemistry.djvu/31

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��INTRODUCTION. chap.

��volume will only be equal to half its former value. That is to say, in the expression

r,dv = A

the value of P has been doubled, whilst the value of dv has been halved; consequently the product remains the same. It is evident that the law is valid for any variation of pressure whatsoever.

Expansion of Gases by Heat at Constant Pressure.— In an analogous manner it can be seen that for a gas which is heated from the absolute temperature T to T+1 the volume changes from Vr = 82^ c.c. to «?,+! = 82 (T + 1) c.c, and the work done on so raising the temperature of a gram-molecule of a gas is —

A = ^^1^ = 1-99 cal.

Expansion of Gases at Constant Temperature.— Let

us consider a gram-molecule at the temperature T and under a pressure of p atmos. ; on expansion the pressure p changes, and the change is inversely proportional to the change of volume V, The work done on expanding from Vq to Vi is obtained by integrating pdv ; that is,

A = / pdv.

From Boyle's law, j^v = pqVq, it follows for a gram-molecule of gas that if po = 1 atmo. = 1*014 megadynes per square centimetre, and if Vq = S2T c.c,

PqVq =pv = 1*99 jT cal.

If we introduce this result into the above expression for A we obtain —

A = 1-99 T ^- cal. = 199^ In ^^ cal. = 1-99^ luteal.

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