CHAPTER XVIII. 



THERMODYNAMICS OF ISOTHERMAL AND ADIABATIC 

 CHANGES. 



Heat taken in when a Body expands Isothermally Heat to a neighbouring Adiabatic 

 the same by all paths Change in Temperature when a Body undergoes a small 

 Adiabatic Change Adiabatics steeper than Isothermals Specific Heats at 

 Constant Pressure and Constant Volume Their Ratio y equal to the Ratio of the 

 Isentropic and Isothermal Elasticities Experimental Determinations of y for 

 Gases Adiabatic Gas Equation Fall of Temperature Upwards with Convective 

 Equilibrium Internal Energy taken up by a Gas in Expanding Comparison 

 of Air Scale with Absolute Scale Generalisation of Indicator Diagram for 

 any Stress and corresponding Strain. 



FROM the two laws of Thermodynamics, which, for reversible cycles, 

 may be stated in the forms 



3=W and (2) l^S = 



we may deduce the temperature changes or the heat developments in 



many alterations of physical con- 

 dition, in terms of the known 

 properties of the bodies affected. 



Some of the results may be 

 obtained by elementary methods, 

 using the indicator and entropy- 

 temperature diagrams. We pro- 

 ceed to obtain several of great 

 importance. 



The Heat taken in when a 

 Body Expands Isothermally. 



Let the body expand at tempera- 

 ture 6 by a small amount dv, its 

 path being represented on the 

 indicator diagram by the element 

 AB of an isothermal in Fig. 163. 

 Then dv is represented by MN. 



Let us make AB part of a Carnot cycle, the lower isothermal DC being 

 at temperature - dd. Produce CD to cut AM in H. If all changes 

 are small, ABCD may be regarded as a parallelogram. We shall equate 

 its area expressed by aid of the Second Law of Thermodynamics to that 

 expressed in terms of the constants of the body. 



Let Q be the work measure of the heat along AB. 



Then ^ = ABCD = AH x MN. 







FIG. 163. 



