thermodynamics- old papers- jntu question papers

Code No: R050211802 Set No. 1
II B.Tech I Semester Regular Examinations, November 2007
THERMODYNAMICS AND KINETICS
(Metallurgy & Material Technology)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Prove the following for a closed system .
For constant volume process Q = mCv (T2 − T1)
For constant pressure process Q =mCp (T2 − T1)
(b) Dierentiate between intensive and extensive properties with examples. [12+4]
2. (a) Claculate the work done for the following reversible process
i. Isobaric
ii. Adiabatic
(b) What are point and path functions ? Give some examples [8+8]
3. (a) Show that d
H
dp  s =
v
(b) Name the intensive and extensive parameters in the entropy representation .
Explain them.
(c) The entropy of hot baked potato decreases as it cools . is this a violation of
the increases of entropy principle ? Explain. [16]
4. (a) Explain the following
i. Gibb’s free energy
ii. Helmholtz function
(b) Prove thatW=n! / (n0! n1! n2!) WhereWis maximum possible arrangements.
[16]
5. (a) State and explain the third law of thermodynamics .what is its importance.
[6]
(b) Derive an expression to show variation of equilibrium constant with tempera-
ture. [10]
6. (a) What the relation between free energy and equilibrium constant for any reac-
tion and explain.
(b) At equilibrium of any reaction what is the relation of free energy change and
equilibrium constant and explain. [16]
7. (a) Explain the Duhrings rule and its importance.
(b) Explain the Truton’s rule and its importance. [16]
8. (a) Explain Zero order reaction.

(b) Explain collision theory of chemical reaction. [16]



Code No: R050211802 Set No. 2
II B.Tech I Semester Regular Examinations, November 2007
THERMODYNAMICS AND KINETICS
(Metallurgy & Material Technology)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) State and explain Zeroth law of thermodynamics.
(b) Distinguish clearly between integral and excess thermodynamic properties.
(c) Explain the limitations of thermodynamics. [6+5+5]
2. (a) Show that internal energy is a function of temperature only.
(b) The internal energy of a closed system is given by U = 100 + 50T+ 0.04T2
in Joules. The heat absorbed Q = 4000 +16T in Joules. ( T is in Kelvin ). If
the system changes from 500 K to 1000 K, what did the work done.
(c) Calculate the work transfer and change in internal energy if the gas is changing
its state from 1 bar, 270 to 20 bar, 4000 C polytropically. [6+6+6]
3. (a) Explain and discuss the importance of Second law of thermodynamics.
(b) i. Eciency of a cyclic process and
ii. Carnot theorem. [8+8]
4. (a) Explain the following
i. Gibb’s free energy
ii. Helmholtz function
(b) Prove thatW=n! / (n0! n1! n2!) WhereWis maximum possible arrangements.
[16]
5. (a) State and explain the third law of thermodynamics .what is its importance.
[6]
(b) Derive an expression to show variation of equilibrium constant with tempera-
ture. [10]
6. (a) ‘Fugacity of a component is equal to its activity for ideal solution’. Say true
or false and explain why is it so.
(b) Derive an expression for the change in the free energy when 1gram mole of a
pure substance goes in solution. [16]
7. (a) Explain the Duhrings rule and its importance.
(b) Explain the Truton’s rule and its importance. [16]
8. (a) Explain the standard free energy change for any reaction. [6]
(b) Determine the equilibrium constant at 250c for the reaction
CH4(g) + H2O(l) ! CO(g) + 3H2(g)
Data: [10]
COMPONENT
0G at 250c
CO(g) -137.8 KJ/mole
CH4 (g) -50.09 KJ/mole
H2O (1) -238.0 KJ/mole


Code No: R050211802 Set No. 3
II B.Tech I Semester Regular Examinations, November 2007
THERMODYNAMICS AND KINETICS
(Metallurgy & Material Technology)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. Define the following :
(a) Extensive property
(b) Charle’s law
(c) State property
(d) Critical temperature. [16]
2. (a) State alternative statement of the first law of thermodynamics .
(b) One mole of an ideal gas expands reversibly and isothermally from an initial
volume of V1 to the final volume of 10V1. During expansion the work done by
the system is 42kJ. If the final pressure is 100 bar, then calculate V1.
(c) What is an adiabatic process and what is an adiabatic system. [4+8+4]
3. (a) Is a process internally reversible and adiabatic, necessarily isocentropic? Ex-
plain.
(b) What is meant by the standard molar entropy of a substance? how are stan-
dard molar entropy are used to calculate the standard entropies of a reactions?
(c) Why are standard molar entropies some times called absolute entropires? Ex-
plain. [16]
4. (a) Explain the deductions of third law of thermodynamics
(b) Explain various methods of calculatation of
SO for a chemical reaction [16]
5. (a) State and explain the third law of thermodynamics .what is its importance.
[6]
(b) Derive an expression to show variation of equilibrium constant with tempera-
ture. [10]
6. (a) What the relation between free energy and equilibrium constant for any reac-
tion and explain.
(b) At equilibrium of any reaction what is the relation of free energy change and
equilibrium constant and explain. [16]
7. (a) From the classius clapeyron equation, derive the following.
Expression for the vapor pressure of liquid metal
Log P=A/T+B where A and B are constants.
(b) The vapor pressure P of liquid A is given by Log P (mm) = -2450/T +6.69
abd that of a solid A by log P(mm)=6947+10.8. Calculate the temperature
at which liquid and solid will have the same vapor pressure. [16]
8. (a) Bring out the important characteristic of a catalyst and explain its action.
(b) Explain the various factors aecting the rate of reaction. [16]
Code No: R050211802 Set No. 4
II B.Tech I Semester Regular Examinations, November 2007
THERMODYNAMICS AND KINETICS
(Metallurgy & Material Technology)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Name few macroscopic modes of energy and a few microscopic modes of energy.
(b) Distingush between study state and equilibrium.
(c) State and explain the criteria which the system should satisfy for it to be in
a thermodynamic equilibrium. [6+5+5]
2. (a) Distinguish between ‘Enthalpy’ and ‘heat capacity’
(b) A student made the following erroneous statement in a laboratory report on
Bomb Calorimetry.
“
H =
E + P
V. Since the bomb calorimetry process is a constant vol-
ume one,
V = 0 and
E =
H. Explain in detail why this arrangement is
incorrect. [6+10]
3. Calculate the standard entropy of a pure iron at 16270C if it’s standard entropy
at 250C is 6.50 Cal / deg / mole. The phase transformation in pure iron may be
represented as follows : [16]
< α−Fe >!< β −Fe >! 9100c < γ −Fe >! 14000c < δ−Fe >! 15390c{Fe}
Given data:
Cp, < α − Fe >= 4.18 + 5.9210−3 T cal/deg/mole
Cp, < β − Fe > = 9.0 cal/deg/mole
Cp, < γ − Fe >= 1.84 + 4.6610−3 T cal/deg/mole
Cp, < δ − Fe > = 10.50 cal/deg/mole
Cp, {Fe} = 10.0 cal/deg/mole
< α − Fe >!< β − Fe >;
H0
7600c = 660 cal/ mole
< β − Fe >!< γ − Fe >;
H0
9100c = 215 cal/mole
< γ − Fe >!< δ − Fe >;
H0
14000c = 165 cal/ mole
< δ − Fe >! {Fe};
H0
15390c = 3670 cal/mole
4. (a) What do you understand by the term free energy of a system. what is its
Significance?
(b) From the first principles, derive the equations for the Gibbs free energy
G =

H − T
S
(c) How can free energy change of a reaction determine experimentally. [16]
5. (a) What do you know about thermo chemical data. [8]
(b) Discuss the use of third law of thermodynamics in evolution of
SO of a
reaction [8]
6. (a) Derive Van ‘tho’s equation for the variation with temperature of equilibrium
constant.
(b) Explain how standard free energy of reaction related to the equilibrium con-
stant of a reaction. [16]
7. (a) Say true or false the following statements with suitable Explanation. Activity
of component can never be greater then unity in a system under equilibrium.
(b) State and explain Troutons rule. [16]
8. (a) Derive an expression for the rate constant of a first order reaction
(b) Discuss the importance of equilibrium constant and its eects on equilibrium
conversion. [16]

thermodynamics-old question papers- jntu

Code No: R05310803 Set No. 4
III B.Tech I Semester Regular Examinations, November 2007
CHEMICAL ENGINEERING THERMODYNAMICS-II
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. Water and a liquid mixture of propane and butane are admitted into a vaporizer at
50 oC and leave as vapors at 175 oC. The hourly 25 kg water, 350 kg propane and
550 kg of butane are admitted. Estimate the heat requirement in the vaporizer.
Component Latent heat of vaporization Boiling point a b×103 C×106
cal/gm mole at 100oC temp Tc
oC
Propane 5038 96.6 8.41 35.95 -6.97
Butane 6138 151.8 2.25 45.40 -8.83
Water 10388 96.6 7.14 2.64 0.046
Cp =a+bT+cT2 where Cp is in cal/mol.k and T is in K. Mention the assumption
made to solve the problem. [16]
2. (a) 40 kg of ethyl alcohol and 50 kg of acetic acid are charged into a reactor to
yield ethyl acetate as per the reaction,
C2H5OH (l) + CH3COOH (l) = C2H5OOCCH3 + H2O
The reaction is 60% complete. Estimate the heat eect of this process heat of
combustion in cal/mol: C2H5OH = -326700; CH3COOH = - 208300; C2H5OOCCH3
= - 538760, H2O(l)= - 68.3 Kcal/gm mole.
(b) Write short notes on eect of temperate on heat of reaction. [10+6]
3. (a) Estimate Z, HR and SR at 70 oC and 200Kpa for an equimolar vapor mixture
of propane and pentane using virial expansions B11 = -276, B22 = -809, B12
= -466 cm3/mol.
(b) Write and explain fundamental residual property relation. [10+6]
4. For Diethyl ether (1) - Chloroform (2) at 30 oC, γ
1 = 0.71 and γ
2 = 0.57, P1
sat =
33.73 kPa and P2
sat = 86.59 kPa. The system is believed to governed by Margules
type of equations for activity coecients. Prepare a p-x-y diagram for the system
at 30 oC. [16]
5. (a) Explain bubble print and dewprint.
(b) Describe the vapor/ liquid equilibrium calculation procedure for DEW P. Va-
por and liquid phases may be considered as non- ideal. [6+10]
6. Show that the residual Gibbs energy of fluids from Redlich-Kwong equation of state
is GR
RT = Z − 1 − ln(1 − h)Z −
Code No: R05310803 Set No. 4
8. For the gas phase reaction CO2 (g) + 2H2 (g) , CH3OH (g) at 10000 C and at
500 bar pressure,calculate the equilibrium composition using the following data:
K = 0.68 at 10000C; The fugacity coecients at this pressure:
CO2 =0.99; H2 = 1.15; CO = 1.08; H2O = 0.86. [16]

thermodynamics old jntu question papers

Code No: R05310803 Set No. 3
III B.Tech I Semester Regular Examinations, November 2007
CHEMICAL ENGINEERING THERMODYNAMICS-II
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. Water and a liquid mixture of propane and butane are admitted into a vaporizer at
50 oC and leave as vapors at 175 oC. The hourly 25 kg water, 350 kg propane and
550 kg of butane are admitted. Estimate the heat requirement in the vaporizer.
Component Latent heat of vaporization Boiling point a b×103 C×106
cal/gm mole at 100oC temp Tc
oC
Propane 5038 96.6 8.41 35.95 -6.97
Butane 6138 151.8 2.25 45.40 -8.83
Water 10388 96.6 7.14 2.64 0.046
Cp =a+bT+cT2 where Cp is in cal/mol.k and T is in K. Mention the assumption
made to solve the problem. [16]
2. Carbon monoxide gas is burned at constant pressure with 100% excess air. The
reactants enter at 25 0C and the exhaust gases leave the reaction chamber at 1200
0C Estimate the heat loss from the reaction chamber
Standard heat of combustion of CO=-282,900 J/mol
Cp =a+bT+cT2 Cp in J/mol-K, T in K
The constants of a, b, c are: [16]
a b×103 c×106
CO2 26.75 42.26 -14.25
N2 27.02 5.81 -0.29
O2 25.29 13.25 -4.20
3. (a) Derive an expression for estimating fugacity of a liquid at a given T and P.
(b) The partial molar volume of methanol in methanol- water. Solution at x1 =
0.3881 (mole fraction) is 39.176 × 10 −6 m3/mol. The density of the mixture
is 905.376 kg/m3. Calculate the partial molar volume of water in the solution.
[8+8]
4. Derive and discuss the Wilson equation as a model of solution behaviour for mul-
ticomponent system. Discuss the merits of this model over others. Explain its
temperature dependence also. [16]
5. (a) Explain bubble print and dewprint.
(b) Describe the vapor/ liquid equilibrium calculation procedure for DEW P. Va-
por and liquid phases may be considered as non- ideal. [6+10]
Code No: R05310803 Set No. 3
6. When the compressibility factor Z is a function of P, T show that the residual
entropy of fluids from virial equation of state is SR
R = −
P
R
dB
dT . [16]
7. Discuss about LLE and draw its solubility diagrams represented in the form of an
‘island’ [16]
8. In a laboratory investigation, acetylene is catalytically hydrogenated to ethylene at
1,1200C And 1 bar. If the feed is an equimolar mixture of acetylene and hydrogen,
what is the composition of the product stream at equilibrium? The reactions are
C2H2 ! 2C + H2
2C + 2H
K1= 4x105, K2 =2.5x10−6. [16]

thermodynamics-old papers-jntu syllabus

Code No: R05310803 Set No. 2
III B.Tech I Semester Regular Examinations, November 2007
CHEMICAL ENGINEERING THERMODYNAMICS-II
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. If the heat capacity of the substance is correctly represented by in equation of the
form, Cp = A + BT + CT2
Show that the error resulting when H is assumed = Cp evaluated at the
arithmetic mean of initial and final temperature is C(T2 − T1)2/12. [16]
2. Calculate the maximum temperature in degree centigrade when the following gas
is burned with 30% excess air entering at 25 0C:
CO 30%
H2 15%
CO2 5%
N2 50%
The mean heat capacities of these gages (in cal/ g mole 0K) are:
CO : 7.587
H2 : 7.138
O2 : 7.941
N2 : 7.507
CO2 :11.92
H2O : 9.39
Heat of combustion data:
Hc (k cal/ g mole) CO = 67.63 and H2O = 68.32. [16]
3. Derive the relation for the calculation of Gibbs free energy of ideal gas mixture,
starting from fundamental property relation. [16]
4. Vapor-liquid equilibrium data for the system 1, 2 dichloro methane (1) /methanol
(2) at 50 oC are as follows:
P/kpa x1 y1
55.55 0.000 0.000
58.79 0.042 0.093
64.59 0.189 0.265
65.76 0.349 0.349
65.59 0.415 0.367
63.86 0.632 0.418
59.03 0.835 0.484
48.41 0.945 0.620
31.10 1.000 1.000

Determine the values of lnγ1 and lnγ2 using Margules equations. Also plot lnγ1 and
lnγ2 Vs x1. [16].
5. The excess Gibbs energy for a binary system is given by: GE/ RT = 0.45 X1 X2.
The pure component vapor pressures are given by:
ln P1
sat/kPa = 14.39−
2795.8
t/oC+230
ln P2
sat/kPa = 16.59−
3644.2
t/oC+239
Obtain the P-x, y diagram for this system at 50oC. [16]
6. Show that the residual Gibbs energy of fluids from Redlich-Kwong equation of state
7. Name the dierent types of binary mixtures in terms of solubility. What are the
thecritical solution temperature and the three phase temperature for a partially
miscible liquid solution. Show them on diagram. [16]
8. Write short notes on:
(a) Eect of temperature on equilibrium constant K
(b) Law of mass action. [8+8]

biochemical thermodynamics-jntu old papers-2008

BIO CHEMICAL THERMODYNAMICS Question Papers (Supple, 2008, Nov)

Posted by m.s.chowdary at 8:10 AM
Monday, December 22, 2008

SET: 1

1. Is it possible to prove the laws of thermodynamics? Describe in brief. (b) One mole of an ideal gas at 1.0MPa and 310K is heated at constant temperature till the volume is doubled again. Calculate the work done by the gas.

2. Name the methods by which the thermodynamic properties of fluids are usually presented. Discuss any two of them.

3. (a) What is the significance of the second law efficiency? (b) Define the second law efficiency of a process.

4. Prove the following:

a) Viid = Vi

b) Hiid = Hi

c) Vid = ΣxiVi

d) Hid =Σ xiHi
5. Show that when Lewis Randall rule is valid for one species in a linery solution, the Henrys law lis is valid for the other one.

6. Rate and equilibrium conversion of a chemical reaction depends of what parameters? How rate and equilibrium conversion varies in various situations. Give a suitable example to explain above.

7. Discuss in detail about the Thermodynamic principles.

8. Explain the aerobic production of a single extracellular product.

SET: 2

1. A reversible engine operating between a reservoir at 600K and the ambient atmosphere at 300K drives a refrigerator operating operating between 240K and the ambient atmosphere. Determine the ratio of energy rejected by both the devices to the ambient atmosphere to the energy absorbed by the engine from the reservoir at 600K.

2. It is desired to design a tank to store 10Kmol methane at 6MPa and 300K. Determine the size of the tank using the Red lich? Kwong equation of state. The critical constants of methane are
Pc = 4.6MPa and Tc = 190.6K.

3. (a) Give an example of a fundamental relation. (b) What is an equation of state? How many eequations of state are there for a single component of simple compressible substance.

4. (a) Discuss in brief heats of mixing, heats of reaction and heats of solution. (b) Show that heats of mixing are generally much smaller than heats of reaction.

5. Show that at equilibrium for a closed system, (dGi)T,P=0.

6. (a) Define reaction coordinate. What is its usefulness?
(b) For a system in which the following reaction occurs CH4 + H2o ---> CO +3H2,assume there are present initially 2mol CH4, 1molH2o, 1mol Co and4molH2. Determine expressions for the mole fraction yi as function of Є

7. (a) Describe the inter relationship amongst the metabolism, energy and redox processes.
(b) Explain the concept that ATP is the energy shuttle in the cell.

8. Discuss theoretical predictions of yield coeffiecients.


SET: 3

1. One mole of an ideal gas ( Υ = 1.4) at 0.5 MPa and 300K (state 1) is heated at constant pressure till volume is downloaded (state 2) and then it is allowed to expand reversibly and adiabatically till the temperature is reduced to 300K (state 3). Calculate the heat and work interactions. If it is desired to restore the system fron state 3 to its original state by a reversible isothermal path, determine the amount of work to be done on the system.

2. (a) What is ideal gas? Name the two basic assumptions, which were made use of in deriving the ideal gas equation of state from kinetic theory arguments. (b) Define thermodynamic properties, classify the thermodynamic properties. What is the use of such classification.

3. A particular thermodynamic system has the following equations of state.

1/T = 5NR/2U; P/T = NR/V

Obtain the third equation of state of the system.

4. (a) Discuss the importance of fugacity in thermodynamics. (b) Discuss fugacity and fugacity coefficient for pure species.

5. (a) For VLE at low to moderate pressures, discuss the nature of equilibrium. (b) For VLE, show that yi ØiP = xi Υi Pisat (i = 1,2,---------N).

6. Consider a system in which the following reaction occur,

CH4 + H2O ----> CO + 3H2 (1)

CH4 + 2H2O ----> CO2 + 4H2 (2)

Where the numbers (1) and (2) indicate the value of is the reaction index if there are present initially 2 mol CH4 and 3 mol H2O. determine expressions for the Yi as function of Є1 and Є2.

7. Discuss in detail about medium formulation.

8. Write short notes on:

(a) Respiratory quotient

(b) Oxidative Phosphorylation.


SET: 4

1. (a) Discuss limitations of first law of thermodynamics. (b) State alternative statements of first law of thermodynamics.

2. (a) What is ideal gas? Name the two basic assumptions, which were made use of in deriving the ideal gas equation of state from kinetic theory arguments. (b) Define thermodynamic properties, classify the thermodynamic properties. What is the use of such classification.

3. Show that for an ideal gas, (dE/dV)T = 0.

4.

5. Prove the following
(a) fi l = fi sat = ФisatPisat
(b) fi = ФisatPisatexp[Vil(P-Psat)/R.T]

6. For the equililnium state of a chemical reaction, show that .−RT lnK = ΔGo.

7. (a) Explain the Gaden classification from stoichiometric point of view the product formation in fermentation process.
(b) The following stoichiometric equation describes penicillin synthesis: 1.5 Glucose + H2SO4 + 2NH3 + phenyl acetate penicillin G + CO2 + 8H2O the theoretical yield of penicillin is 1.2g (gram of glucose). Find out the molecular weight of penicillin G

8. Discus in detail the heat evolved per equivalent of available electrons transferred to oxygen.

thermodynamics-jntu-oldquestionpapers

Code No: R05310803 Set No. 1
III B.Tech I Semester Regular Examinations, November 2007
CHEMICAL ENGINEERING THERMODYNAMICS-II
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) The latent heat of vaporization of ethyl alcohol is experimentally to be 200
cal/gm. at its normal BP of 78 0C. Its critical temperature is 243 oC. Estimate
the heat of vaporization at a temperature of 180 oC.
(b) Define of heat of solution based on one mole of solution and one mole of solute.
Also derive the relationship between them. [6+10]
2. The gas stream from a sulphur burner is composed of 45 mol % SO2, and 55 mol%
O2. This gas stream at 1 bar and 480 oC enters a catalytic converter when SO2
is further oxidized to SO3. Assuming that the reaction reaches equilibrium, deter-
mine how much heat must be removed from the converter to maintain isothermal
conditions per 100 mol of entering gas Cp / R = A + BT +D/T2 [16]
A 103 B 10−5 D
Hf, 25oC
Gof, 25oC
J/mol J/mol
SO2 5.699 0.801 -1.015 -296830 -300194
O2 3.639 0.506 -0.227 - - - - - - - - - -
SO3 8.060 1.056 -2.028 -395720 -371060
3. (a) Discuss the determination of fugacity from equation of state, with special
reference to Vander waals gas and show that, ln f = ln (RT/(V-b)) + b/(V-b)
? 2a/RTV.
(b) Show mathematically that the entropy change on mixing is not zero even for
ideal gases. [12+4]
4. (a) Elucidate the vapor-liquid equilibrium of binary systems with the help of p-x-y
and t-x-y diagrams.
(b) Write and explain models for excess Gibbs energy based on the local compo-
sition. [12+4]
5. (a) Discuss the phase rule and Duhem’s theorem for non-reacting system, explain
in detail.
(b) The binary system of benzene (1) / ethyl benzene (2) conforms closely to
Raoult’s law. Vapor pressures for the pure species are given by the following
Antoine equations:
ln p1
sat/kpa = 13.8594 −
2773.78
t/0C+220.07
ln p2
sat/kpa = 14.0045 −
3279.47
t/0C+213.2
Prepare P-xy diagram for a temperature of 900C. [6+10]
Code No: R05310803 Set No. 1
6. Determine expressions for GR, HR, SR implied by the vander waals equation of
state. [16]
7. Develop equations that apply to the limiting case of binary LLE for which the
α-phase is very dilute in spices 1 and the β-phase is very dilute in species2. [16]
8. A mixture of N2, H2 and Argon in the mole ratio 1:3:2 enters a catalytic reactor
for the synthesis of ammonia. The reactor is maintained at 400oC and 20 Mpa.
Estimate the degree of conversion (K = 1096104). [16