Thermodynamics Questions and Answers

1 gm of ice at 0 C is mixed with 2 gm of water at 90 C Find the final temperature specific heat capacity of water 1 cal gm C and latent heat of fusion of ice 80 cal gm Options 1 2 3 20 C 100 C 3 40 3 0 C 30 C

A tyre pumped to a pressure of 2 atmosphere suddenly bursts If the temperature of air before expansion is 27 C then the final temperature of air is useCP 1 5 2 1 2 Cv Options 1 2 2 3 23 C 23 C 27 C 27 C

The work output and heat input involved by a system in process A are 20 kJ and 15 kJ respectively Another process B between the same end conditions involves a heat input of 10 kJ Determine the change in internal energy involved and also the work done in process B Show that if a cycle is formed using processes A and B the given data is consistent with the first law

closed system having a mass of 50 kg has an initial velocity of 10 m s Subsequently its velocity increases to 30 m s and its elevation also rises by 40 m During this process the system receives 30000 J of heat and 4500 J of work If the system delivers 0 002 kWh of electrical energy make calculations for a change in the internal energy of the system

A circular wire of radius R placed on a horizontal smooth surface is made t rotate about a fixed vertical axis passing through its center as shown If break ing stress of the material of wire is So then maximum value of so that wir NS A 42R2 find the value of N Cross sectional are does not break is given by of wire is A is the linear mass density of wire R

of law of thermodynamics A Enegy can neither be created nor be destroy B The total energy of the universe remains constant C Enthalpy change depends only upon initial and final state

A closed system undergoes a thermodynamic cycle consisting of four separate and distinct processes The heat and work transferred in each process are as tabulated below Work transfer in kJ min 10 500 Process Heat transfer in kJ min 1 2 0 30 000 3 000 9 000 Show that the data is consistent with the first law of thermodynamics and proceed to evaluate the net work output in kW thermal efficiency of the cycle and the change in internal energy for each process 2 3 3 4 0 30 000 1 500

The given P V diagram represents the thermodynamic cycle of an engine operating with an ideal monoatomic gas The net workdone by the gas in one cycle is P 2Pg A P V 11 C P V V 2V0 V 13 B 12 P V D 4 P V

Suppose one mole of an ideal gas undergoes the reversible cycle ABCA shown in the P V diagram above where AB is an isotherm The molar heat capacities are C at constant pressure and Cv at constant volume The net heat added to the gas during the cycle is equal to PA P P C A Th To B

In an ideal Brayton cycle air from the atmosphere at 1 atm 300K is compressed to 6 atm and the maximum cycle temperature is limited to 1100K by using a large air fuel ratio If the heat supply is 100 MW find a the thermal efficiency of the cycle b work ratio c power output and d the mass flow rate

A thermal machine operates under the ideal Rankin cycle the temperature in the boiler is 2000K The water vapor enters the boiler at 9MPa and 120C comes out at 9MPa and 800C The mass flow of vapor through the boilers is 5kg s If the heat is rejected at a speed of 4500kJ s in the condenser and the drain s temperature is 27C determine A the thermal efficiency of the cycle B the maximum power that might give the machine under the same conditions of the boiler

An ideal monatomic gas is taken through a thermodynamic process from A to B as shown Heat supplied to the gas in the process is P 2Pot 1 3P V 5PV Pot A Vo B 2 2 5P V 3PV V

Question 22 7 joules of heat is required to raise the temperature of an ideal diatomic gas A 7 5 at constant pressure from 30 C to 35 C amount of heat required in joule to raise the temperature of same gas through the same range at constant volume in joule

A hydrogen like atom atomic number Z is in higher excited state of quantum number n This excited atom can make a transition to the first excited state by successively emitting two photons of energy 22 95 eV and 5 15 eV respectively Alternatively the atom from the same excited state can make transition to the second excited state by successively emitting two photons of energies 2 4 eV and 8 7 eV respectively What will be the value of Z 2 3

5 5 6 a A horizontal drum belt drive carries the belt over a semicircle around it The drum has a diameter of 1 m and when it rotates 400 Nm of torque is transmitted The drum has a mass of 25 kg and the coefficient of friction between the belt and drum is 0 25 Neglecting mass of belt determine tensions induced in the limbs of the belt and the verticle reaction on the bearings

The curved path in Fig 18 23 lies on the 350 K isotherm for an deal gas with y 1 4 a Calculate the net work done on the gas as it goes around the cyclic path ABCA b How much heat lows into or out of the gas on the segment AB Pressure p kPa 250 200 150 100 50 0 D Volume V L B

b Water enters at the outer cylinder co axial double pipe heat exchanger at 40 C and leaves at 70 C hot gases enter inner cylinder at 305 C and leaves at 170 C If the circumference of the inner pipe is 1000 mm length is 500 m and the over all heat transfer coefficient is 600 W m C determine the total heat transfer for i Parallel flow Counter current flow 11 If in parallel flow same amount of heat is to be exchanged as that of counter current flow what will be the heat transfer area

A closed piston cylinder device contains 0 5 kg of carbon dioxide CO initially at 300 K and 100 kPa The carbon dioxide is now slowly expanding in an isobaric process to a final volume of 1 m3 a Determine the volume in m3 of the CO2 at the initial state choose nearest value from below Multiple Choice 0 284 m3 0 375 m 0426m

c A heat engine employing Carnot s cycle with an efficiency n 20 is used as a refrigerating machine the thermal reservoirs being the same Find the coefficient of performance of the machine 6

A cube of ice of mass 49 gm at 0 C is placed in an adiabatic container having negligible heat capacity and 100 gm water at 32 C Ice melts but maintains a cubical shape Find the volume of ice cube outside in cc water in steady state Pice 0 9 gm cc

Example 3 10 A system contains 0 15 m of a gas at a pressure of 3 8 bar and 150 C It is xpanded adiabatically till the pressure falls to 1 bar The gas is then heated at a constant pressure ll its enthalpy increases by 70 kJ Determine the total work done Take c 1 kJ kg K and c 0 714 J kg K P

c Calculate the entropy change when 3 g of ice is converted into steam and is then heated to 140 C under constant pressure Given that specific heat of water 4180 J kg K Latent heat of ice 3 35 x 10 J kg 1 Latent heat of steam 2 26 x 106 J kg Specific heat of steam 2 x 10 J kg K 5

efficiency in terms of temperatures of its heat reservoirs b The efficiency of a Carnot s engine is 40 when the temperature of the sink is 27 C What is the temperature of the source In order to raise its efficiency to 50 what do you think ou of the following two is more effective way 6

b The efficiency of a Carnot s engine is 40 when the temperature of the sink is 27 C What is the temperature of the source In order to raise its efficiency to 50 what do you think out of the following two is more effective way i Decreasing the temperature of the sink while the temperature of the source remains the same ii Increasing the temperature of the source while the temperature of the sink remains the same Justify your answer 6 75

b Show that the heat transferred during an infinitesimal quasistatic process of an ideal gas can be written as SQ CV vdp VdP nR where n denotes the number of moles and R is the Gas Constant Apply the above equation to an adiabatic process to show that PVY constant 8 75 Cp pdv nR

A closed system undergoes a change of state by process 1 2 for which Q 10J and W 2 5J The system now returns to its original state by different path 2 1 for which Q2 3J The work done by the gas is a 8J b 0J c 2J d 5J

A standing wave is formed in a long tube by a tuning fork of frequency 500 Hz kept at its open end and other end is closed b a movable piston as shown in the figure A resonance is produced when 18 0 cm 55 5 cm and 93 0 cm respectivley The temperature of air is maintained at 77 C and molecular weight of air is 28 8 10 kg mol Choose the correct option s C Piston Long Tube The minimum distance between node and antinode is 18 75 cm The speed of wave in the tube is approximately 375 m s The adiabatic coefficient of air inside the tube is approximately 1 39 There is an end correction of 0 75 cm

Answer to each question will be evaluated according to the following marking scheme Full Marks 3 If ONLY the correct option is chosen Zero Marks 0 In all other cases A standing wave with a frequency of 1100Hz in a column of methane at 27 0 C produces consecutive nodes that are 0 200 m apart What is the approximate value of y for methane The molar 25 mass of methane is 16 0 g mol Take R 3 J mol K O 715 4 3 6 5 5 3

A particle of mass m and charge q is tied to a string of length L in gravity free space A uniform electric field E is applied as shown in the figure If the particle is slightly displaced perpendicular to length of string then the time period of small oscillations will be 1 2n L E m q 2 2n mL 3qE

For an ideal gas the change in internal energy in a constant pressure process from temperature T to T is equal to nCv T2 T where Cy is the molar specific heat at constant volume and n the number of moles of the gas the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process the internal energy does not change in an isothermal process Ono heat is added or removed in an adiabatic process

e bulb of a mercury thermometer is placed first in melting ice at standard pressure then in mam at standard pressure and at last in a liquid X The lengths of mercury thread in the uniform De above bulb in the three cases are 30 mm 180 mm and 60 mm respectively What is the mperature of X an option 20 C BPC 29 4 C

A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities K and K The equivalent conductivity of the combination is T A B BHU 2001 MP PET 2007 NEET 2017 K K K K 2 2K K K K d K K 2K K K K T

A cylindrical isotropic solid of coefficient of linear expansion and density p floats in a liquid of coefficient volume expansion y and density d as shown in the diagram 1 5 Glob lw med re Column I A volume of cylinder inside the liquid remains constant B volume of cylinder outside the liquid remains constant C Height of cylinder outside the liquid remains constant D Height of cylinder inside the liquid remain constant PTC Column Ilolote A p y 0 mumbavi grT q y 2a r y 3a d Puika d s y 2a a 000 A gr hi P

half of its volume If P V and I represent the pressure volume and temperature of the gaseous system respectively then the correct equation representing the process is A TV 2 5 constant B C VP5 3 constant TP 2 5 Correct Answer constant

One mole of a diatomic gas is taken from P to Q Q to R and R to S If the total work done by the gas is All and change in internal energy of the gas in whole process is AU then PA 3Po 2Po Po V 21 21 V

Steam locomotives have an efficiency of 19 0 and operate with a hot steam temperature of 475 C a What would the cold reservoir temperature in C be if this were a Carnot engine 141 1485 X C b What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150 C 196

0 Zeroth Law 1 First Law 2 Second Law 3 Third Law A skier is riding on a surface ski lift Suddenly he loses grip from the seat and starts sliding down the va There is a cup of tea you forgot to drink To know the temperature of the tea you put the head of a digi thermometer on the exterior part of the cup with no need to wet it 2 In molecular gastronomy alternative techniques are widely used to reach extreme temperatures For iquid nitrogen helps to stop the cooking process of foods at the right moment A pot full of water is covered with a lid and is left on a hot stove When you hear the lid making noise now that it s time to add pasta 1 While playing a videogame on your laptop the laptop gets very hot in it have the same temperatu

44 p T diagram was obtained when a given mass of gas was heated During the heating process from the state 1 to state 2 the volume P 0 1 a remained constant b decreased c increased d changa arraticall 2 T

54 A steady current of 1 5 A flows throug voltameter for 10 minutes If the elect equivalent of copper is 30 x 10 5 g cou mass of copper deposited on the electr AIPMT Prel 2 0 40 g 4 0 67 g 1 0 27 g 3 0 50 g

In which process does the heat capacity not depend on the parameters and is always equal to infinity Which one is always zero Express the heat capacity of the process in terms of entropy

Two moles of helium gas are taken over the cycle ABCDA as shown in the P T diagram Use In2 0 7 P Pa 4x105 2 105 A B D 300K A The work done by the gas from A to B is 600R B The work done by the gas from B to C is 840R C The net work done by the gas in the cycle ABCDA is 276R D The net work done on the gas in the cycle ABCDA is 1076R C 600K T

Two mechanical waves y 2 sin 2 50 t 2x y 4 sin 2m ax 100 t propagate in a medium wit same speed 1 The ratio of their intensities is 1 16 3 The value of a is 4 units 2 The ratio of their intensities is 1 4 4 The value of a is 2 units

A steel rod at 25 C is bolted at both ends and then cooled By how many C should the rod be cooled so N that it will rupture Assume that till rupture Hooke s law is obeyed If your answer is N fill value of Osteel 10 x 10 C Y 2 10 N m and o breaking stress of steel rod 4 x 108 N m 40

0 02 moles of an ideal gas undergo a cycle consisting of an isochoric process an isobaric process and an isothermal process as shown below Volumes and pressures at specific points are indicated on the axes The pressure in atm at point B is X The value of 10X is P atm A B 50 C 100 V cm

A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in figure Its volume is then reduced to the original value from E to F by an isobaric process If the total work done by the gas from D to E to F is 10 in J then find the value of k D 1200 Pressure P N m 100 0 T 2 Volume V m T E

Copper has a coefficient of volume expansion of 51 x 109 1 C A copper kettle is at 23 0 C When the water inside and kettle is heated 100 C the volume of the kettle expands by 1 08 x 10 5 m What is the volume of the kettle at 23 0 C O 2 75 x 10 3 m O 3 40 x 103 m O 1 26 x 103 m O 1 99 x 103 m O 4 34 x 10 3 m

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98 The pressure and density of a diatomic gas Q 98 va face the x 7 change adiabatically from P p to P p If 128 then is equal to 1 128 2 32 1 32 3 1 128 4 Gal 1 128 1 128 3 ufa P P 735 128 P p P p fafda ARTER 2 at and Gren 2 32 1 32 4

41 shown in figure P4 B A D increasing d None of the above P gas is AQ wi 1730 a during the process AB work done by the gas is positive b during the process AB work done by the gas is negative gas is c during the process BC internal energy of the hore coefficient of performance is

Consider a thermodynamic system which goes from i to T through the process shown in figure here Then work is done h D By the system through out the path ABF By the system for path AB and on the system for path Br By the system for path iA and on the system for path ABf On the system throughout the path IABf Volume