Thermal Analysis Exam 1

An air compressor has a gage pressure of 166 psig and the surrounding

environment is at 35 psia. What is the absolute pressure of the air

compressor tank?

Pabs = Pg + Ps

Pabs = 166 psig + 35 psia

Pabs = 201 psia

A water pump that consumes 2 kW of electric power when operating is

claimed to take in water from a lake and pump it to a pool whose free

surface is 30 m above the free surface of the lake at a rate of 50 L/s.

Determine if this claim is reasonable.

𝑚̇ = 𝜌𝑉̇

p = 1000 kg/m³

V = 50L/s => 0.05 m³/s

𝑚̇ = 50 kg/s

𝑊̇𝑝𝑢𝑚𝑝 = 𝐸̇𝑚𝑒𝑐ℎ,𝑓𝑙𝑢𝑖𝑑 = 𝑚̇ 𝑔Δ𝑧

50 × 9.81 × 30 = 14715 W

= 14.7 kW

not reasonable

An oil pump is drawing 44 kW of electric power while pumping oil with ρ

= 860 𝑘𝑔/𝑚³ at a rate of 0.1 𝑚³/𝑠 . The inlet and outlet diameters of the pipe are

8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is

measured to be 500 kPa and the motor efficiency is 90 percent, determine

the mechanical efficiency of the pump.

Δ𝐸̇𝑚𝑒𝑐ℎ,𝑓𝑙𝑢𝑖𝑑 = 1/2 𝑚̇ (𝑣²_2 − 𝑣²_1) + ((𝑃_2−𝑃_1)𝑚̇)/𝜌

𝑚̇ = 𝜌𝑉̇

𝑚̇ = 86 kg/m³

𝑽̇ = 𝑣 × 𝐴

𝑣 = 𝑽̇ /𝐴

A= (pi d²)/4

plug all in and

= 36332 W or 36.332 kW

𝑊̇pump,shaft = 𝜂motor*𝑊̇electric = (0.90)(44kW) = 39.6kW

36.3/39.6 = 91.8%

In a hydroelectric power plant, 65 m3/s of water flows from an elevation

of 90 m to a turbine, where electric power is generated. The overall

efficiency of the turbine–generator is 84 percent. Disregarding frictional

losses in piping, estimate the electric power output of this plant.

e_mech = gz

9.81 m/s² * 90 m = 0.8829 kJ/kg

𝑚̇ = 𝜌𝑉̇ = 1000× 65 kg/s = 65000 kg/s

𝑊̇max = 65000 kg/s * 0.8829 kJ/kg

= 57.39 MW

57.39 × 84% = 48.2 MW

Both a gage and a manometer are attached to a gas tank to measure its

pressure. If the reading on the pressure gage is 80 kPa, determine the

distance between the fluid levels of the manometer if the fluid is (a)

Mercury (𝜌 = 13600 𝑘𝑔/𝑚³) or (b) water (𝜌 = 1000 𝑘𝑔/𝑚³). Gravitational

acceleration is 9.8 m/s²

P1 = Ps +pgh

P1 = 80kpa +Patm

80kpa +Patm = Patm +pgh

80,000 Pa = pgh

solve for h with given

h_merc = 0.60 m

h_water = 8.16 m

A paddle wheel does 10,000 Nm work on a system where the initial

energy of the system was 10 kJ. If the system gains 15 kJ of heat from a

heat source and loses 3 kJ due to heat loss during the process, find the

final energy of the system.

Δ𝐸𝑠𝑦𝑠𝑡𝑒𝑚 = 𝐸𝑖𝑛 − 𝐸𝑜𝑢𝑡 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 + 𝑊𝑖𝑛 − 𝑊𝑜𝑢𝑡

= 15 − 3 + 10 − 0 𝑘𝐽

= 22 𝑘𝐽

Δ𝐸𝑠𝑦𝑠𝑡𝑒𝑚 = 𝐸𝑓𝑖𝑛𝑎𝑙 − 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙

𝐸𝑓𝑖𝑛𝑎𝑙 = 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 + Δ𝐸𝑠𝑦𝑠𝑡𝑒𝑚

= 10 + 22 𝑘𝐽

= 32 𝑘𝐽

A piston cylinder system contains water at 500 kPa and 350o C. The

system is compressed and cooled until the pressure reaches 5000 kPa. At

this state, the internal energy is measured to be 333.82 kJ/kg. Determine:

a. Phase at initial state

b. Enthalpy at initial state

c. Phase at final state

d. Temperature at final state

Given, T1=350 C, P1=500 kPa

From table A-5, for Psat=500 kPa, Tsat,500kPa=151.83 C

a. Here, T1>Tsat,500kPa, therefore initial phase is superheated vapor.

b. Table A-6, T1=350 oC, P1=500 kPa, h1=3168.1 kJ/kg

c. P2=5000 kPa (5 MPa), u2=333.82 kJ/kg

From Table A-5, for Psat=5000 kPa, uf= 1148 kJ/kg, ug=2597 kJ/kg

Therefore, u2<uf, so we have compressed liquid.

d. From Table A-7, P2=5 MPa, u2=333.82 kJ/kg

So, T2= 80o C

10 kg of R-134a at 300 kPa fills a rigid container whose volume is 14 L.

Determine the temperature and total enthalpy in the container. The

container is now heated until the pressure is 600 kPa. Determine the

temperature and total enthalpy when the heating is completed.

a)

1 + 0.25 = 1.25 atm

1.25 × 101.325

P = 126,656.25 atm

b)

21.35 + 273.15 = 294.5 k

c)

v=V/m => 2/3 m³/kg

d)

Pv = R*T

R = Pv/T

(126656 ×2/3) / 294.5

R = 286.7 T/kg k

E = mgh

E = 1029 kJ/s

m_turb = 800/1029 => 77.7%

n_turb,gen = 750/1029 => 72.8%

a) temp at state 1

99.61

b) quality at state 1

x = 0

c) phase of state 2

p = 100 kPa

v = 1 m³/kg

saturated mixture (in between)

d) quality of phase 2

(1 - 0.001043)/(1.6941 - 0.00143) = 0.590

e) internal energy at state 2

417.9 + (0.59×2088.2)

f) phase at state 3

superheated vapor (1.9367>1.6941)

g) temp at state 3

150

h) internal energy at state 3

2582.9 kJ/kg