aku thermodynamics question paper

Aryabhatta knowledge university

  Sem. iv   2013                               Time 3hr                            Full marks: 70

Thermodynamics                        

Attempt any five question in which question no 1 is compulsory

1.       Choose the correct answer (any seven):

(a)    In case of free expansion between state -1 and state -2 ,which of the following is correct considering no heat interaction?

(i)                  U₁ =U₂

(ii)                W_1-2 =0

(iii)               Q_1-2 =0

(iv)              All of the above

(b)   The latent heat of vaporisation with increase in pressure of water

(i)                  Increases

(ii)                Remains constant

(iii)               Decreses

(iv)              None of the above

(c)    As differentials heat and work would be described mathematically as

(i)                  Inexact

(ii)                Exact

(iii)               Discontinuity

(iv)              Point function

(d)   Heat is being supplied to air in a cylinder fitted with a frictionless piston held by a constant weight, the process is

(i)                  Isochoric

(ii)                Isobaric

(iii)               Adiabatic

(iv)              Isothermal

(e)   Expansion of hot gases in an IC engine can be approximated to an

(i)                  Isochoric

(ii)                Isobaric

(iii)               Adiabatic

(iv)              Isothermal

(f)     A refrigerator and a heat pump operate between same temperature limits. If the COP of refrigerator is 4, then the COP of heat pump is

(i)                  3

(ii)                4

(iii)               4.4

(iv)              5

(g)    A relation of vapour to enthalpy of vapourisation is expressed in

(i)                  van der walls equation

(ii)                Maxwell equation

(iii)               Carrier equation

(iv)              Clausius-clapeyron equation

(h)   For same maximum pressure and temperature among Otto , diesel and dual cycles

(i)                  diesel cycle is most efficient

(ii)                 Otto cycle is most efficient

(iii)                dual cycle is most efficient

(iv)              None of the above

(i)      Thermal efficiency of rankine cycle can be improved by steam

(i)      Reheating

(ii)     super heating

(iii)   Regeneration

(iv)  None of the above

(j)     The process of removing moisture from air at constant dry bulb temperature is known as

(i)                  Sensible heating

(ii)                Sensible cooling

(iii)               Dehumification

(iv)              Humidification

2.       (a) define internal energy. Show that internal energy is a property of a system.

(b) a cylinder contains 0.12 m³ of air at 1 bar and 90°c .It is compressed to 0.03 m³ .The final pressure being 6 bar .Find the index of compression, increase in internal energy and heat transferred. Take R= 0.287 KJ/kg-K and C_v=0.717KJ/kg-K

3.       (a)  prove the Kelvin planck and Clausius statement of the second law of thermodynamics are equivalent to each other.

(b)  A reversed Carnot Cycle operating as a refrigerator has a capacity of 100 KJ/s while operating  between temperature limits of -20°c and 35°C. Determine (i) power input and (ii) COP . What would be its efficiency if it runs as an engine?

4.       (a)  state and prove Clausius inequality.

(b)  During isothermal heat addition process of a Carnot cycle, 800 KJ heat is added to the working fluid from a source of 527°c. Determine  (i) change in entropy of the working fluid , (ii) change in entropy of the source and (iii)  total entropy change during the process.

5.       (a)  define the following:

(i)                  Pure substance

(ii)                Saturation point

(iii)               Triple point and critical point

 (b) A vessel of volume 0.04m³ contains a mixture of saturated water and saturated steam at temp  of 250°C. The mass of liquid is 9 kg . Find the enthalpy and the internal energy .

6.       In an air -standard dual cycle, the pressure and temperature at beginning of compression are 1 bar and 57°C respectively. The heat supplied in the cycle is 1250 KJ/kg, two third of this being added at constant volume and rest at constant pressure. If the compression ratio is 16, determine the air-standard efficiency.

7.       (a) give limitation of carnot vapour power cycle and explain how Rankine cycle helps in overcoming them.

(b) A stem power plant running on Rankine cycle has steam entering HP turbine at 20MPa, 500°c and leaving LP turbine at 90% dryness. Considering condenser pressure of 0.005 MPa and reheating occurring up to the temperature of 500°C , determine  the thermal efficiency of the cycle.

8.       (a) what do you mean by dry bulb and wet bulb temperatures? When do d.b.t. ,w.b.t.and d.p.t. become equal?

(b) 10 m³ /min of air at 1 atm and 20°C with 90% RH is mixed with 20 m³  /min of air at 1 atm and 40°C with 20% Rh. Calculate the resulting state of mixture.

9.        (a) Explain Maxwelll relation in thermodynamics .

(b) A gaseous mixture consists of 1 kg of oxygen and 2 Kg of nitrogen at a pressure of 150 Kpa and a temperature of 20°C . Determine the change in internal energy and enthalpy of the mixture when the mixture is heated to a temperature of 100°C (i) at constant volume and (ii) constant pressure.

Mechanics of solid-1

Aryabhatta Knowledge University

  Sem. iv   2013                               Time 3hr                            Full marks: 70

Mechanics of solid-1                        

Attempt any five questions in which question no 1 is compulsory

1.       Answer any seven from the following in short:

(a)    Explain internal and external forces.

(b)   Discuss generalized Hooke’s law.

(c)    Define the terms ‘longitudinal strain’, ‘lateral strain’ and ‘poison’s ratio’.

(d)   What do you mean by strain energy?  Illustrate clearly with suitable example.

(e)   How do you find the maximum bending moment in a beam?

(f)     How can you determine the maximum instantaneous deflection of a beam subjected to impact loading?

(g)    Define the term ‘pure torsion’.

(h)   Distinguish between major and minor principal stresses.

(i)      State the criteria for a thin cylinder. What types of stresses are induced in a thin cylindrical shell subjected to an internal pressure?

(j)     Define helical spring .name the two important types of helical springs.

2.       A steel bolt of 12 mm diameter passes through a brass tube of 16 mm diameter, 25 cm long and 20 mm external diameter. The bolt is tightened by nut at 15 degree Celsius so as to exert a compressive force 1500 kg on the tube .calculate the stress in each (a) 15 degree Celsius (b) when the temperature of the tube and bolt is raised to 50 degree Celsius.

Take

E_ѕ =2х10⁶kg/cm²

 α_s= 12х10^-6/°c

E_b = 1х10⁶kg/cm²

α_b= 19х10^-6/°c

3.       Derive the torsion formula

T∕J=Ƭ∕r=Gθ/L

With assumption where all terms indicate usual meanings.

4.       A close –coiled helical spring, consisting of 8 coils , each having mean diameter 80 mm  and wire diameter 10 mm . The spring is fixed at one end and twisting moment of 10 Nm applied axially at other end in such a way that the spring tends to open . Determine (a) the maximum bending stress produced in the wire of the spring ,(b)the angle of twist ,(c) the resistance and (d) the number of turns after the application of torque. Take, E=2х10^5N/mm^2.

5.       Show that in a strained material under two dimensional stress system , the sum of normal  components of stresses acting on any two mutually perpendicular planes is constant . the principal stresses at a point in a strained material are √(σ₁²+σ₂²)/2

6.       Cast iron T section having overall depth 150 mm, flange and web 30 mm is used as bracket. The length of the bracket is 300mm. If the tensile stress is restricted to 20 n/mm² , what will then be placed at the top of bracket ? What will then be the compressive stress developed?

7.       Draw the shear force ,bending moment and axial force diagrams for the beam supported and loaded as shown in the figure below:

8.       A cantilever AB of 6 m length is subjected to a u.d.l. of intensity w t/m spread over the entire length. Assuming rectangular cross section with depth equal to twice breadth , determine the minimum dimensions of the beam so that the vertical deflection at  the free end of does not exceed 1.5 cm and the maximum bending stress does not exceed 1000 kg/cm²  .Take E=2 x 10⁶ kg/cm²

9.       Two round bars of varying diameter A and B are shown in Fig . Below made of same material. An axial blow on bar A produces a maximum stress of 100 N/mm².Find the maximum stress produced by the same blow on the bar B. If the bar B is also stressed to 100 N/mm², find the ratio of strain energies stored in the bars A and B.

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ARYABHATTA KNOWLEDGE UNIVERSITY

NUMERICAL METHOD AND COMPUTATIONAL TECHNIQUE

  Sem. iv   2013                                    Time 3hr                        Full marks: 70

Attempt any five questions in which question no 1 is compulsory

1.       Answer any seven from the following:

                (a)            In C++ ,a mathematical expression 137% 10 yields

(i)                  13

(ii)                13.7

(iii)               0

(iv)              7

               (b)            Which of the following statements is true about the break statement?

(i)                  A break statement causes an exit only from the innermost loop

(ii)                A break statement causes an exit only from the innermost switch

(iii)               A break statement causes an exit only from all loops and switches

(iv)              A break statement causes an exit from the innermost loop or switches

                (c)            What is the process of converting one predefined type into another called?

(i)                  Type casting

(ii)                Expression

(iii)               Type promotion

(iv)              Type conversion

               (d)            The assignment statement a-=b; can also be written as

(i)                  a=b-1

(ii)                a=a-b

(iii)               a=a-(-b)

(iv)              a=b-a

               (e)            the operator which is used to access the address of a variable is

(i)                  &

(ii)                #

(iii)               @

(iv)              *

                 (f)            What do you mean by a difference equation?

                (g)            Define the order and degree of a difference equation with examples.

               (h)            What is the difference between an initial value problem and a boundary value problem ?

                  (i)            What do you mean by the order of convergence of an iterative method for finding the root of the equation f(x)=0 ?

                 (j)            When is the convergence of an iterative method for solving the equation f(x)=0 said to be (i) linear and (ii) quadratic?

2.       (a) find the root of the equation xtanx=1.28, that lies between 0 and 1, correct to two  places    of decimals, by bisection method

(b) Write a computer program using C/ C++ for the above equation using bisection method.

3.       (a) Find the Newton- raphson iterative formula for the reciprocal of a number N and hence find the value of 1/23, correct to 5 decimals.

(b) Write a computer program using C/C++ to find the smallest positive root /the largest negative root of the equation f(x)=0 , by using the simple iterative method.

4.       Solve the following system of equations by Jacobi’s iteration method and gauss-seidel’s method:

10x₁+2x₂ +x₃=3

X₁+ 10x₂- x₃=-22

-2X₁+3x2+10 x₃=22

5.       The population of a town Patna in the census is as given in the data. Estimate  the population in the year 1996 using Newton’s forward interpolation and backward interpolation formulae:

Year(x)	1961	1971	1981	1991	2001
Population (in 1000’s approx)	46	66	81	93	101

6.       (a) fit a curve of the form xy= a+bx² to the following data by the method of least square :

X	1	2	4	6	8
Y	5.43	6.28	10.32	14.86	19.51

 (b) Write a computer program using C/C++ to fit a straight line of the form xy=a bx² taking the above data, using the method of least square.

7.       The velocity of a particle at distance s from a point on its linear path is given in the following data :

S(m)	0	2.5	5.0	7.5	10.0	12.5	15.0	17.5	20.5
V(m/sec)	16	19	21	22	20	17	13	11	9

Estimate the time taken by the particle to traverse the distance of 20 meters , using Simpson’s one-third rule.

8.       (a) Find the value of y(1.1) ,using runge-kutta method of the fourth order , given that dy/dx=y² +xy ;y(1)=1

(b) Write a computer program using C/c++ to solve the above differential equation at specified pivotal points, using runge –kutta method of the fourth order.

9.       Solve the boundary value problem v’’(x)- xy(x)=0 for x_i=0, 1/3 ,2/3 , given that y(0)+y’(0)=1 and y(1)=1.