Modern Engineering Thermodynamics

138 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
Now, we incorporate our earlier results that 1 W 2 = 0andu 2 − u 1 = c v (T 2 − T 1 ) = 0, because T 2 = T 1 here (the
process is also isothermal). Our latest rendition of the problem statement makes it clear that V 2 = V 1 ,andwhen
these conditions are incorporated into the energy balance, we obtain our final equation for the heat transfer as
1Q 2 = m 0 + 0 + gðZ
2 − Z 1 Þ
g
+ 0 = mg
c
g
ðZ 2 − Z 1 Þ
system
c
and, from the equation of state, we can determine the solution to part (b) as
since T 2 = T 1 and v 2 = v 1 .
p 2 = RT 2 /v 2 = RT 1 /v 2 = RT 1 /v 1 = p 1
Step 7 allows us to calculate the values of the unknowns:
ðaÞ 1 Q 2 = ð5:00 kgÞð9:81 m/s2 Þ
ð0 − 50:0mÞ = −2450 kg.m 2 /s 2
1
= −2450 N ⋅ m = −2450 J = −2:45 kJ
and
ðbÞ p 2 = p 1 = 0:300 MPa
The negative sign in the answer for part (a) tells us that the heat transfer is out of the system. Note that the
answer in part (b) was not the result of a complex calculation. However, it did result from a rather complex analysis
and, therefore, is not trivial. Also note that we did not need the value of v 2 in the solution of the problem,
so it would have been a waste of time to have calculated it early in the solution.
In step 8, since the solution now seems to work well, the problem statement is complete and accurate. We
should now check all the algebra, units, and calculations before creating and solving additional problems with
similar or different scenarios.
Exercises for the problem solved in Steps 1–8
1. Rewrite this problem and make the barrel insulated but not isothermal. (Can it be both insulated and
isothermal?) Resolve the problem with these new conditions. Is any additional information needed to find
T 2 and p 2 ?
2. Write a thermodynamics problem about a computer chip. Look up the steady state voltage and current
required by a typical computer chip in a handbook and supply these values in the problem statement. This
is a closed system, and the chip cannot be insulated (otherwise, it would overheat). Use the energy rate
balance in the formulation of your problem scenario.
3. Write a thermodynamics problem about an electrical generator. Use the closed system energy rate balance.
Make the process steady state. You may have the generator insulated or uninsulated. Note that there are two
work modes here, shaft work and electrical work.
4. Write a thermodynamics problem about an airplane. Make it a closed system and have it change altitude and
speed. Choose an appropriate unknown and provide all the necessary values for the remaining variables.
SUMMARY
In this chapter, we discover that the first law of thermodynamics is simply the conservation of energy principle.
Since energy is conserved in all actions, the change in a system’s energy can be equated to the net transport of
energy into the system. Only three possible energy transport mechanisms are available to us: (1) heat transport
of energy (commonly called heat transfer), (2) work transport of energy (commonly called work), and (3) energy
transported with a mass flowing across a system’s boundary. This information produced the very powerful
energy balance and energy rate balance equations.
The general closed system energy balance:
The general closed system energy rate balance:
1Q 2 − 1 W 2 = ðE 2 − E 1 Þ system
= m½ðu 2 − u 1 Þ + ðV 2 2 − V2 1 Þ/ð2g cÞ + ðZ 2 − Z 1 Þg/g c Š system
_Q − _W = ðdE/dtÞ system
= ðm _u + mV _V /g c + mg _Z/g c Þ system