Thermodynamics and Propulsion

2.6 Muddiest Points on Chapter 2

MP 2..1   What are the conventions for work and heat in the first law?

Heat is positive if it is given to the system. Work is positive if it is done by the system.

MP 2..2   When does $E\rightarrow U$ ?

We deal with changes in energy. When the changes in the other types of energy (kinetic, potential, strain, etc.) can be neglected compared to the changes in thermal energy, then it is a good approximation to use $\Delta U$ as representing the total energy change.

MP 2..3   When is enthalpy the same in initial and final states?

Initial and final stagnation enthalpy is the same if the flow is steady and if there is no net shaft work plus heat transfer. If the change in kinetic energy is negligible, the initial and final enthalpy is the same. The “tank problem” is unsteady so the initial and final enthalpies are not the same. See the discussion of the steady flow energy equation in notes, Section 2.5.

MP 2..4   In the filling of a tank, why (physically) is the final temperature in the tank higher than the initial temperature?

Work is done on the system, which in this problem is the mass of gas that is pushed into the tank.

MP 2..5   What is shaft work?

I am not sure how best to answer, but it appears that the difficulty people are having might be associated with being able to know when one can say that shaft work occurs. There are several features of a process that produces (or absorbs) shaft work. First of all the view taken of the process is one of control volume, rather than control mass (see the discussion of control volumes in Chapter I or in IAW). Second, there needs to be a shaft or equivalent device (a moving belt, a row of blades) that can be identified as the work carrier. Third, the shaft work is work over and above the ``flow work'' that is done by (or received by) the streams that exit and enter the control volume.

MP 2..6   What distinguishes shaft work from other works?

The term shaft work arises in using a control volume approach. As we have defined it, ``shaft work'' is all work over and above work associated with the ``flow work'' (the work done by pressure forces). Generally this means work done by rotating machinery, which is carried by a shaft from the control volume to the outside world. There could also be work over and above the pressure force work done by shear stresses at the boundaries of the control volume, but this is seldom important if the control boundary is normal to the flow direction.

If we consider a system (a mass of fixed identity, say a blob of gas) flowing through some device, neglecting the effects of raising or lowering the blob the only mode of work would be the work to compress the blob. This would be true even if the blob were flowing through a turbine or compressor. (In doing this we are focusing on the same material as it undergoes the unsteady compression or expansion processes in the device, rather than looking at a control volume, through which mass passes.)

The question about shaft work and non shaft work has been asked several times. I am not sure how best to answer, but it appears that the difficulty people are having might be associated with being able to know when one can say that shaft work occurs. There are several features of a process that produces (or absorbs) shaft work. First of all, the view taken of the process is one of control volume, rather than control mass (see the discussion of control volumes in Section 2.5 or in IAW). Second, there needs to be a shaft or equivalent device (a moving belt, a row of blades) that can be identified as the work carrier. Third, the shaft work is work over and above the flow work that is done by (or received by) the streams that exit and enter the control volume.

MP 2..7   Definition of a control volume.

A control volume is an enclosure that separates a quantity of matter from the surroundings or environment. The enclosure does not necessarily have to consist of a solid boundary like the walls of a vessel. It is only necessary that the enclosure forms a closed surface and that its properties are defined everywhere. An enclosure may transmit heat or be a heat insulator. It may be deformable and thus capable of transmitting work to the system. It may also be capable of transmitting mass.

MP 2..8   What is the difference between enthalpy and stagnation enthalpy?

The enthalpy of a gas is defined as $h = u + pv = u + p/\rho$ , and represents both the internal energy of that state and the flow work done on the gas to get it at that pressure and density. The stagnation enthalpy of a gas is defined as $h_t = h + c^2/2$ and accounts for both the enthalpy and the kinetic energy of the gas at that state.