PR Termodinamika Teknik Kimia-1 B dan C.

Semester Ganjil 2015/2016.

Catatan: PR dikumpulkan pada saat UTS Termodinamika

1. The reading on a mercury manometer at 25˚C (open to the atmosphere at one end) is 56.38

cm. The local acceleration of gravity is 9.832 m/s2. Atmospheric pressure is 101.78 kPa.

What is the absolute pressure in kPa being measured? The density of mercury at 25˚C is

13.534 g/cm3.

2. The variation of fluid pressure with height is described by the differential equation:

dP

dz= −ρg

Here, ρ is specific density and g is the local acceleration of gravity. For an ideal gas, ρ =𝑀𝑃

𝑅𝑇, where M is molar mass and R is the universal gas constant. Modeling the atmosphere

as an isothermal column of ideal gas at 10˚C, estimate the ambient pressure in Denver,

where z = 1 mille relative to sea level. For air, take M = 29 gram/mole while value of R is

given in Appendix A (Smith & van Ness).

3. A gas is confined in a 0.47 m diameter cylinder by a piston, on which rests a weight. The

mass of the piston and weight together is 150 kg. The local acceleration of gravity is 9.812

m/s2 and atmospheric pressure is 101.57 kPa.

a. What is the force in Newton exerted on the gas by the atmosphere, the piston and the

weight assuming no friction between the piston and cylinder?

b. What is the pressure of the gas in kPa?

c. If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If

the piston and weight are raised 0.83 cm, what is the work done by the gas in kJ? What

is the change in potential energy of the piston and weight?

4. An egg is initially at rest is dropped onto a concrete surface and breaks. With egg treated as

the system,

a. What is the sign of Q, W, ∆Ep and ∆Ek?

b. What is ∆Ut?

In modelling this process, assume the passage of sufficient time for the broken egg to

return to its initial temperature. What is the origin of the heat transfer of part (e)?

5. One mole of gas in a closed system undergoes a four-step thermodynamics cycle. Use the

data given in the following table to determine numerical values for the missing quantities,

i.e., ‘fill in the blanks’

Step ∆Ut/s Q/s W/s

12

23

34

41

-200

?

?

4700

?

-3800

-800

?

-6000

?

300

?

12341 ? ? -1400

6. A non-conducting container filled with 25 kg of water at 20˚C is fitted with a stirrer which

is made to turn by a gravity acting on a weight of mass 35 kg. The weight falls slowly

through a distance of 5 m in driving the stirrer. Assuming that all work done on the weight

is transferred to the water and the local acceleration of gravity is 9.8 m/s2, determine:

a. The amount of work done on the water.

b. The internal energy change of the water.

c. The temperature of the water, for Cp = 4.18 kJ/ (kg ˚C).

d. The amount of the heat must be removed from the water to return it to its initial

temperature.

e. The total energy change of the universe because of:

(1) The process of lowering the weight

(2) The process of cooling the water back to its initial temperature

(3) Both process together

7. A closed non-reactive system contains species 1 and 2 in vapour/liquid equilibrium.

Species 2 is very light gas, essentially insoluble in the liquid phase. The vapour phase

contains both species 1 and 2. Some additional moles of species 2 are added to the system,

which is then restored to its initial T and P. As a result of the process, does the total

number of moles of liquid increase, decrease or remain unchanged?

8. Gas is bled from a tank. Neglecting heat transfer between the gas and the tank, show the

mass and energy balances produce the differential equation:

𝑑𝑈

𝐻′ − 𝑈 =

𝑑𝑚

𝑚

Here, U and m refer to the gas remaining in the tank; H’ is the specific enthalpy of the

gas leaving the tank. Under what conditions can one assume H’=H?

9. Fifty (50) kmol per hour of air is compressed from P1=1.2 bar to P2=6.0 bar in a steady

flow compressor. Delivered mechanical power is 98.8 kW. Temperatures and velocity

are:

T1= 300 K T2=520 K

u1=10 m/s u2=3.5 m/s

Estimate the rate of heat transfer from the compressor. Assume for air that Cp=7/2 R and

that enthalpy is independent of pressure.

10. Steam flows at steady state through a converging, insulated nozzle, 25 cm long and with

an inlet diameter of 5 cm. At the nozzle entrance (state 1), the temperature and pressure

are 325C and 700 kPa, and the velocity is 30 m/s. At the nozzle exit (state 2) the steam

temperature and pressure are 240C and 350 kPa. Property value are:

H1= 3,112.5 kJ/kg V1= 388.61 cm3/g

H2= 2,945.7 kJ/kg V2= 667.75 cm3/g

What is the velocity of the steam at the nozzle exit, and what is the exit diameter?

11. Find the equation for the work of a reversible, isothermal compression of 1 mol of gas in

a piston/cylinder assembly if the molar volume of the gas is given by

𝑉 =𝑅𝑇

𝑃+ 𝑏

Where b and R are positive constants.

12. The conditions of a gas change in a steady flow process from 20C and 1,000 kPa to

60C and 100 kPa. Devise a reversible non flow process (any number of steps) for

accomplishing this change of state, and calculate ∆U and ∆H for the process on the basis

of 1 mol of gas. Assume for the gas that PV/T is constant, Cv=(5/2)R, and Cp=(7/2)R.

13. A tank of 0.1 m3 volume contains air at 25C and 101.33 kPa. The tank is connected to a

compressed air line which supplies air at the constant conditions of 45C and 1,500 kPa.

A valve in the line is cracked so that air flows slowly into the tank until the pressure

equals the line pressure. If the process occurs slowly enough that the temperature in the

tank remains at 25C, how much heat is lost from the tank? Assume air to be an ideal gas

for which Cp=(7/2)R.

14. Calculate Z and V for ethylene at 25C and 12 bar by the following equations:

a) The truncated virial equation (Eq.(3.40)) with the following experimental values of

virial coefficients:

B=-140 cm3 mol

-1 C=7,200 cm

6 mol

-2

b) The truncated virial equation (Eq.(3.38)), with a value of B from the generalized

Pitzer correlation (Eq.(3.63))

c) The Redlich/Kwong equation

d) The soave/Redlich/Kwong equation

e) The Peng/Robinson equation

15. Natural gas (assume pure methane) is delivered to a city via pipeline at a volumetric rate

of 150 million standard cubic feet per day. Average delivery conditions are 50F and 300

psia. Determine:

a) The volumetric delivery rate in actual cubic feet per day

b) The molar delivery rate in kmol per hour

c) The gas velocity at delivery conditions in m/s

The pipe is 24 in schedule 40 steel with an inside diameter of 22.624 in. standard

conditions are 60F and 1 atm.

16. Ammonia is to be isothermally compressed in a specially designed flow turbine from 1

bar and 100oC to 50 bar. If the compression is done reversibly, compute the heat and

work flows needed per mole of ammonia if:

a) ammonia is assumed as an ideal gas,

b) ammonia follows equation of state: P(v-b) = RT, with b = 3.730x10-3

m3/kmol

17. A 100 m3 of CO2 initially at 150

oC and 50 bar is to be adiabatically compressed in a

frictionless piston and cylinder device to a final pressure of 300 bar. Calculate:

a) the volume and temperature of the compressed gas;

b) the work done to compress the gas;

Assuming CO2 is:

i. an ideal gas,

ii. a real gas, following virial equation.

18. Sifat fisis fluida X mengikuti persamaan dibawah ini:

𝑈 = −0,015 + 0,720 ∗ 𝑇; dan 𝑃𝑉 = 0,287 ∗ 𝑇

Dimana: U [=] internal energi spesifik, dalam kJ/kg; T [=] suhu, dalam K; P [=] tekanan,

dalam kN/m2; V [=] volume spesifik, dalam m

3/kg. Sebuah sistem yang terdiri atas

sebuah mesin silinder dengan piston tanpa friksi berisi fluida X ini, mengalami ekspansi

adiabatis mengikuti persamaan: PVδ = konstan, dari tekanan 1 MPa , dan suhunya turun

dari 100oC menjadi 30

oC. Dimana δ = (Cp/Cv). Berapakah tekanan akhir dari sistem

tersebut?

oOo - oOo