244 Mr Searle, The Expansion of a Gas, etc. 



| 2. The determination of the specific heat at constant pressure 



for gases. 



In the experimental determination of the specific heat of a 

 gas at constant pressure, the gas is sent through a spiral tube 

 immersed in water in a calorimeter, and the temperature of the 

 gas before and after passing through the tube is observed as well 

 as the rate of change of the temperature of the water in the 

 calorimeter. When the pressure of the gas is the same on both 

 sides of the spiral, the experiment gives the specific heat of 

 the gas directly, but, in practice, there must be a small difference 

 of pressure, and thus some small correction becomes necessary. 



The process is really an extreme case of the "porous plug" 

 experiment, and is best considered from the point of view of that 

 experiment. 



We may begin with the case of a " perfect " gas, i.e. a gas 

 obeying Boyle's law and having its internal energy dependent only 

 upon its temperature. The second of these conditions implies that 

 dUjdv t is zero. Thus, by (3) 



t^=p. 



Integrating, we have 



log p + G (v) = log t, 



or pF(v) = t, 



where G(v) and F(v) are functions of v alone. But, since Boyle's 

 law is obeyed, F(v) = v/R, where R is a constant. The charac- 

 teristic equation is therefore 



pv = Rt (8). 



Since U is a function of t alone, we may write 



*-% :«* 



It is unnecessary to add a subscript v to the differential coefficient 

 to show that v is constant during the differentiation, because U is 

 independent of v. 



If we equate the heat absorbed, when the gas is heated at 

 constant pressure, to the sum of the energy gained by the gas and 

 the work done by it, we have 



~ 7i dU 7 , dv 7 , 

 Updt = —j- dt+p-j— dt, 



so that C p = G v + p -j— 



dtp 



= C V + R (10). 



