Adiabatic Reversible Changes

Corollary. In all reversible adiabatic changes the entropy remains constant such changes are therefore isentropic changes. 

The other extreme case is the adiabatic change, which occurs with no heat transfer between the gas and the surroundings. For a reversible adiabatic change, k = y where y = Cp/Cv, the ratio of the specific heat capacities at constant pressure (Cp) and at constant volume (C ). For a reversible adiabatic change of an ideal gas, equation 6.27 becomes... 

In a reversible adiabatic change the entropy remains constant and therefore this type of change is called an isentropic change. Although not rigorously valid for irreversible changes, equations 6.32 to 6.34 are good approximations for these conditions. 

Putting k = y gives an approximate equation for adiabatic flow. The result is only approximate because it implies an isentropic change, ie a reversible adiabatic change, but this is not the case owing to friction. A rigorous solution for adiabatic flow is given in Section 6.5. 

Equation 6.19 is the basic equation relating the pressure drop to the flow rate. The difficulty that arises in the case of adiabatic flow is that the equation of state is unknown. The relationship, PVy = constant, is valid for a reversible adiabatic change but flow with friction is irreversible. Thus a difficulty arises in determining the integral in equation 6.19 an alternative method of finding an expression for dPIV is sought. 

INVERTED MICELLE REVERSE TRANSCRIPTASE VIRAL POLYMERASES Reversible adiabatic change,... 

Entropy remains constant for arty reversible adiabatic change so that dS = 0. 

We can derive an expression for a reversible, adiabatic change from Vj to V2 and from Tj to T2 by summing (integrating) the infinitesimal changes required ... 

For many purposes it is more useful to develop an expression relating the temperature to the pressure in a reversible, adiabatic change. Since an ideal gas is under consideration, it follows that P Vi = RTi and P%V2 = RTt if these equations are combined with (10.5) so as to eliminate Vi and Vt, it is found that... 

The only constant-entropy changes of state for a perfect gas are reversible adiabatic changes, for which pVr = const... 

In an adiabatic expansion of a gas, mechanical work is done by the gas as its volume increases and the gas temperature falls. For an ideal gas undergoing a reversible adiabatic change it can be shown that pvy=Ki V p -r=K2... 

Response of v to changes in P. Changes of volume in response to changes in pressure are given by the compressibilities. Two are in common use one for isothermal changes Kj and the other for reversible adiabatic changes Kg,... 

Path B- C The system undergoes a reversible adiabatic change that does work on the surroundings and reduces the system temperature to Tq. 

Path D- A The system undergoes a reversible adiabatic change in which work is done on the system, the temperature remrns to Th, and the system returns to its initial state to complete the cycle. 

Solution During the reversible adiabatic changes, the change in entropy is zero. Hence the S-T diagram is as shown. 

Consider a gas undergoing a reversible, adiabatic change in volume. Such changes are not isothermal, but you can still use equation 2.49. Plot the final pressure of 1.00 mole of ideal gas at 1.00 bar initial pressure as the volume increases. Also plot the isothermal final pressure as volume increases from the same initial conditions (that is, Boyle s law). How do these two plots compare ... 

Therefore, considering a reversible, adiabatic change of state, the differential dU of the internal energy per mole of gas is... 

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