CONTRIBUTIONS TO THERMODYNAMICS: THE SPECIFIC HEAT OF AN IDEAL GAS
IT SEEMS of interest to establish upper and lower limits for the specific heat of the generalized ideal gas, so that for any particular gas an approximate value may be readily estimated. The work reported in this paper establishes these limits. MINIMUM SPECIFIC HEAT
Consider a stream of gas passing along through a pipe. Approximately neglect the effects of friction and viscosity. If we consider a particular section, of fixed volume, then in a particular increment of time a mass of gas m in a volume Vl will be forced into that section a t the pressure pl. It will expand somewhat in passing through, and the mass m will leave as a volume V2 at the lower pressure p2. The net work done is p,T.i - plVl. But for an ideal gas p l V , = pzVz, so that the net work done is zero. In the steady state there is no change in the internal energy ( U ) in this constant-volume section of the pipe; that is, dU = 0. Since dU = dq - dw, where dq is the increment of heat added to the system and dw is the increment of work done by the system, and since both dU and dw
are zero, therefore dq = 0 and the process is adiabatic. In an adiabatic expansion, the internal energy of the gas will fall, and the temperature will decrease: energy is used in expanding the gas. For an ideal gas, dU = C,dT, where C, is the specific heat a t constant volume and d T is the increment of temperature. But in the process we are considerine. dU = 0. Therefore. since the temperature falls ( d T g n o t zero), C. must be zero. This gives the minimum value for C.. MAXIMUM SPECIFIC HEAT
Consider unit mass of the gas flowing through the pipe. Accelerate it so it flows faster. Then you have done work on it, and this work is converted into kinetic energy. We know that dU = dq - dw = C.dT for an ideal gas. There is no heat flow in the present process, so dq = 0. There is no temperature change, so d T = 0. But work was done, so dU = - dw and is greater than zero (an increase in kinetic energy). But if dU is greater than zero and is equal to C d T , and also d T = 0, then C , must equal infinity. This gives the maximum value for the specific heat. Dr. Seagel of our laboratories has pointed out that, EDITOR'SNOTE: This is the first of a short series of articles having established the upper and lower limits, i t is by an unknown "Dr. McQuirg," to test our readers' insight and ingenuity. After trying ta find out what is the matter with his now only necessary to interpolate in order to obtain a numerical value for C,. reasoning, turn to the comment on page 325.
