HW 3 and HW 4 common mistakes, notes

Hi everyone,

A few common problems people faced in HW 3:

1. Integrating dW = PdV correctly to find the work done:

For constant volume processes, W = 0. (If the process is also adiabatic, Q = 0 and therefore delta(U) = 0 by First Law).

When there is work done, we use an equation of state (EOS) or similar relation to find P as a function of V so that we can integrate the equation, e.g. for an ideal gas we use P = RT/V and obtain the equation W = R.T. ln(V2/V1). If you have a different EOS as in Problem 12, you have to use the appropriate relation for P as a function of V.

2. Sign convention for work/heat:

Be very careful about the sign! I noticed a lot of errors (especially when you add up work done or heat associated with multi-step processes) due to incorrect sign. Remember, work done by a system (i.e. expansion work) is positive and work done on a system (i.e. compression work) is negative.

now, on to HW 4:

Open vs. closed systems: with regard to Problem 17:

You cannot apply the relations derived for adiabatic closed systems to relate T2 to T1 in this case! There is continuous mass flow in and out of the system, and that is an immediate indication that you have to perform mass and energy balances for the open system. This will allow you to calculate the change in enthalpy as a function of change in flows, work done, heat inputs, etc. The enthalpy, of course, depends on the state variables (P and T) and this will let you find their values.

Energy balance units:

You have to convert all the terms in the equation to the same system of units. Note that the delta(u^2) terms has units of m^2/s^2, which is equivalent to J/kg. If your enthalpy units are kJ/kg, you must convert before plugging into the energy balance equation or your answers will be way off.

Finally, I was a bit disappointed to see answers on Problem 18 with exit diameters greater than 6 cm. The problem statement itself specifies that the system has a converging nozzle, i.e. D2 MUST be less than D1! If your calculations say otherwise, they are obviously wrong and you should try to find the error. Common sense is your biggest ally while performing engineering calculations.

Good luck on the midterm.
Badri