ISOTHERMAL AND ADIABATIC CHANGES. 



303 



Let us now see how the wire can be taken round a Carnot cycle. 

 Let AB, DC represent neighbouring isothermals at and dO. Let 

 AD, BC represent adiabatics. We draw these steeper for we may expect 

 the change in tension for given stretch to be greater if no heat is 

 allowed to pass, i.e. if we introduce a constraint and the results obtained 

 confirm the supposition. We may take ABCD to represent a Carnot 

 cycle. But we must note that since work is done by the body in con- 

 tracting we must go round counter-clockwise to get a balance of work 

 done by the body in returning to the starting-point. Heat is taken in 



Fia 171. 



along AB and given out along CD, and an adiabatic stretch along AD 

 cools the wire. 



Just as in the case of the pressure- volume diagram, it can be shown 

 that the heat along AB is 



where ds is the change in length along AB, and J3 is the change in length 

 under constant load per 1 rise in temperature. If a is the ordinary co- 

 efficient of expansion, X the temperature coefficient of Young's modulus, 

 and s the total stretch up to A, we may put (3 = a + Xs. 



Similarly the change in temperature under adiabatic change of pull 



when p is the density, K P the specific heat under constant pull probably 

 nearly the same as the specific heat under no pull and Y # is the adiabatic 



