Thermodynamics Questions and Answers

Two cylinders contain same amount of ideal monatomic gas Same amount of heat is given to two cylinders If temperature rise in cylinder A is To then temperature rise in cylinder B will be 1 To 3 3 2 To IN STO To 2 4 5 To Free piston Fixed piston To Heat Heat

During one cycle the working fluid in an engine engages in two work interactions 15 kJ to the fluid and 44 kJ from the fluid and three heat interactions two of which are known 75 kJ to the fluid and 40 kJ from the fluid Evaluate the magnitude and direction of the third heat transfer A body of weight 100N rests on a rough horizontal surface u 0

Tixed In a thermodynamic process mass of a gas is changed in such a manner that the gas releases 20 J of heat when 8 J of work was done on the gas If the initial internal energy of the gas was 30 J then the final internal energy will be 1 2 J 2 18 J 3 42 I 4 58 1

When heat enters from surounding into system is always O Negative O Positive O Neutral In flow work changes Pressure O Volume O Temperature 1 poi 1 poi

Total energy content in system 1 point is mostly contain O U W O U H O U Q The property heat mostly related to O Temperature difference Pressure difference O Volume difference 1 point

When Process goes from initial 1 point to final state is called as O Forward O Backward O Cyclic Some processes are return back to initial state are called as O Cyclic O Irreversible 1 point

An ideal gas containing n moles whose ratio of specific heats is 59 39 undergoes a change according to the relation P Po a V where Po and a are positive constants When the temperature is doubled from an initial value of 2a nR the heat absorbed by the gas is Q find Q a You can use ln 3 1 10

An ideal gas undergoes a process such that P T The molar heat capacity of this process is 33 24 J mol K A The work done by the gas is 2RAT B Degree of freedom of the gas is 4 C Degree of freedom of the gas is 3 for the gas is 1 5 D Y ste

An ideal gas undergoes a process such that Px T The molar heat capacity of this process is 33 24 J mol K A The work done by the gas is 2RAT B Degree of freedom of the gas is 4 C Degree of freedom of the gas is 3 Cp for the gas is 1 5 D Y

A spherical bubble inside water has radius R Take the pressure inside the bubble and the water pressure to be po The bubble now gets compressed radially in an adiabatic manner so that its radius becomes R a For a R the magnitude of the work done in the process is given by 4mpoRa X where X is a constant and y Cp Cy 41 30 The value of X is

II Attempt any four sub parts each question carries 1 mark 1X4 4 5 Carnot engine is an ideal heat engine which converts heat energy into mechanical energy Efficiency of Carnot engine is given by n 1 T T Where T is the temperature of source and T is temperature of sink If Q is the amount of heat absorbed cycle from source Q is the amount of heat rejected cycle to the sink and W is the amount of useful work done cycle then W Q Q and Q Q T T With the help of the passage given above choose the most appropriate alternative for each of the following questions i A Carnot engine absorbs 6x10 cal At 227 C Heat rejected to the sink at 127 C is a 6x10 cal b 4 8x10 cal c 4x 10 cal d 5x10 cal ii Work done cycle by the engine in the above question is a 5 04x10 J b 5 04x10 cal d 4 8x105 J c 4 8x10 cal iii Efficiency of the engine in the above question is a 30 b 10 d 80 c 20 iv At what temperature should the sink be maintained to increase the efficiency by 10 a 77K c 300 C What should be the temperature of the source to increase the efficiency to 30 a 298 4 C b 298 4K V b 300K d 77 C

The pressure and volume of a gas are changed as shown in the P V diagram in this figure The temperature of the gas will P A D B C V 1 increase as it goes from A to B 2 increase as it goes from B to C 3 remain constant during these changes 4 decrease as it goes from D to A

6 A composite bar of 20 mm x 20 mm cross section is made up of three flat bars as shown in Fig 1 74 All the three bars are rigidly connected at the ends when the temperature is 20 C Determine i the stresses developed in each bar when the temperature of the composite bar is raised to 60 C 20 mm STEEL ALUMINIUM STEEL 20 mm 8mm 4 mm 8 mm Fig 1 74 ii the final stresses in each bar when a load of 17 6 kN is applied to the composite bar E 80 GPa a 11 x 10 6 C E 200 GPa a 22 x 10 6 C

Column I contains a list of processes involving expansion of an ideal gas Match this with Column II describing the thermodynamic change during this process Indicate your answer by darkening the appropriate bubbles of the 4 x 5 matrix given in the ORS c NH L 3IG f i UHI HIfda Uch i fa 13 Usa NA GR i Qall ch ch nh l HI2I3Hichi flall AAYI 342 372 4 5 30y Matt Hege uzkia AR Column l a An insulated container has two chambers separated by a valve Chamber I contains an ideal gas and the Chamber II has vacuum The valve is opened 55 ef Affaa 1 Ideal gas 3 ych ded a4 54 cha An ideal monoatomic gas expands to twice its original volume such that its pressure P x where V is the volume of b the gas Yc 352f Y MURHYG NA Vacuum Aafa 34 d y ac 34 GR Gura stat f Px V V2 An ideal monoatomic gas expands to twice its original volume such that its pressure P x 1 V 4 3 where V is its volume C K 3G f U HIU AH P q 34 ggr guka ata Px V 4 3 1 r An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph AY A 3 Ruka stat f P teny SR V 2V V S V r r Column II S The temperature of the gas decreases The qremains constant temperature of the gas increases or The gas loses heat A The gas gains heat Internal energy of gas t decreases Rh

A two stroke cycle diesel engine compression ignition internal combustion engine of a large ship has eight cylinders each of 900 mm bore and with a stroke of 2400 mm The BMEP of each cylinder is 15 bar and the engine runs at 95 rev min with a specific fuel oil consumption of 0 2 kg kWh The calorific value of the fuel oil is 43 000 kJ kg Evaluate the performance characteristics of the engine by determining a the brake power of the engine in MW b the fuel consumption of the engine in tonne h the broke thermal efficiency of the engine

13 One mole of an ideal gas is taken from state A to state B by three different processes Qls Disp P C B D E A V i ACB ii ADB iii AEB as shown in the P V diagram The heat absorbed by the gas is a greater in process ii than in i

11 An ideal gas undergoes a hypothetical cyclic process as follows P Pressure V Volume PA a V Now choose the correct statement 1 During process ab temperature increases 2 Temperature decreases during process bc 3 During process ca temperature decreases

In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B an amount of work equal to 104 6 J is done on the system If this gas is taken from state A to B via a process in which the net heat absorbed by the system is 35 cal how much is net work done by the system in later case 1 cal 4 19 J NCERT Pg 321 1 192 7 J 2 89 6 J

An adiabatic cylindrical vessel is divided into three compartments by two adiabatic pistons connected by a rigid rod Compartments 1 and 3 each contain the same ideal gas y 1 5 at initial pressure volume and temperatures as shown in figure Now the gas in compartment 1 is slowly heated until its volume becomes 4V The final temperature of the gas contained in compartment 3 will be 1 To 3 To 1 Po Vo To 0 eeee 2 Po 4Vo To 0 3 rigid rod 2 2T OT

Two samples A and B of the same gas have equal volumes and pressures The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume If the work done by the gas is the same for the two cases then y specific heat satisfies the equation 1 2 1 y 1 In2 2 1 2 1 1 y In2 3 21 1 In2 4 1 21 1 y In2

If a gas is allowed to expand adiabatically against external pressure O There is decrease in internal energy of gas Pressure remains constant O Its temperature remains constant O There is increase in its internal energy of gas

is 11 An ideal gas of adiabatic exponent Y 5 expanding at constant pressure The ratio of dQ dU dW is Symbols have their usual meanings NCERT Pg 309 1 7 5 1 2 7 2 58 S 3 2 1 1

4 Which of the following is incorrect NCERT Pg 305 1 If two systems A and B are in thermal equilibrium with system C separately then A and B will be in thermal equilibrium 2 Zeroth law of thermodynamics defines temperature 3 Temperature does not determine the direction of flow of heat when two bodies are placed in thermal contact 4 Internal energy of an ideal gas depends on the state of the system

The internal energy of a gas is 20 J It undergoes a thermodynamic process such that 35 J of heat is added to the system and it does 5 J of work on atmosphere The final value of the internal energy of the gas is 1 10 J 3 50 J 2 25 J 4 40 J

No 19 An ideal gas goes from state A to state B via three different processes as indicated in the P V diagram If Q Q2 Q3 indicate the heat absorbed by the gas along the three processes and AUX AU2 AU3 indicate the change in internal energy along the three processos respectively then 1 2 Correct Answer 3 Your Answer 2 Status incorrect Q Q2 Q3 and AU AU2 AU3 Q3 Q2 Q and AU AU2 AU3 Q Q2 Q3 and AU1 A2 A3 Q3 Q2 Q and AU AU2 AU3

3 A and B 4 Only E 5 A Carnot engine with sink s temperature at 17 C has 50 efficiency By how much should its source temperature be changed to increases its efficiency to 60 1 225 K 3 580 K 2 128 K 4 145 K 15 17 60 fa fa fa m 1 225 K 3 580 K ar 50 f 1 wa mitu 2 128 K 4 145 K alled t

Solvelancer Test If a single viral particle of corona virus contains 10 spikes then calculate the total number of spikes in 5 moles of corona virus Solvelancer Test a 6 x 1027 b 3 x 1028 c 3 x 1027 d 6 x 1028

ree moles of an ideal monoatomic gas perform a cycle shown in figure The gas temperature in different states are T 200 K T 400 K T3 1600 K and T4 800 K The work done in 25 J mol K by the gas during the cycle is Take R 3 PA 2 10

Three moles of an ideal gas are in a rigid cubical box with sides of length 0 170 m The ratio of the forces that the gas exerts on each of the six sides of the box when the gas temperature are 27 C and 127 C is A 6 1 C 3 1 E 1 3 B 1 2 D 3 4

Which process will increase the temperature of the system without heating it Adiabatic compression 79 attempts 48 1 got it right Adiabatic expansion Isothermal compression Correct 28s avg time

The average kinetic energy of a monoatomic gas molecule kept at temperature 27 C is Boltzmann constant k 1 3 10 23 JK A 5 85 x 10 21 J B 4 12 x 10 21 J C 3 75 x 10 21 J D 2 85 x 10 21 J E 7 55 x 10 21 J

Two parallel metal plates are 3mm apart and have a uniform electric field strength 500 Vm between them The potential difference between the plates is 1 15 Volt Val 2 166 7 Volt 115 Volt

One end of horizontal thick wire of length 2L and radius 2R is connected to one end of another horizontal wire of length L and radius R If equal forces are applied across two ends then ratio of elongation in the two wires is 3 12 2 73 13 2 4 2

65 In a typical lightning flash a ch transferred between two points at a potentia difference of 10 volt If all the energy released could be used to melt ice at 0 C the amount o ice melted in grams is 1 8 93 10 2 9 107

9 36 An ideal gas is taken through series of changes ABCA The amount of work involved in the cycle is A PA 4P 1 P 1 1 12P V 3 3P V 1 C 1 B V 3V V 1 1 2 6P V 4 P V

gure shows a cyclic process ABCDBEA performed on an ideal gas If PA 2 atm PB 4 5 atm and Pc 6 atm VE 0 05 litre find the work done by the gas in J in the complete process in nearest integer 1 atm pressure 1 x 105 Pa V VA E A 103 P P Po

24 The specific heat of many solids at low temperatures varies with absolute temperature T according to the relation S AT3 where A is a constant The heat energy required to raise the temperature of a mass m of such a solid from T 0 to T 20 K is a 4 x 104 mA c 8 x 106 mA b 2 x 10 mA d 2 x 106 mA

Q29 A double pan window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m and thickness 0 01 m separated by 0 05 m thick stagnant air space In the steady state the room glass interface and the glass outdoor interface are at constant temperatures of 27 C and 0 C respectively The thermal conductivity of glass is 0 8 Wm K and of air 0 08 Wm K Answer the following questions a Calculate the temperature of the inner glass air interface b Calculate the temperature of the outer glass air interface c Calculate the rate of flow of heat through the window

8 A quantity of a substance in a closed system is made to undergo a reversible process from an initial volume of 3 m and initial pressure 105 N m to a final volume of 5 m If the pressure is proportional to the square of the volume i e P AV the work done by the substance will be a 3 6 102 J c 2 2 104 J b 2 4 x 10 J 3 6 x 105 Ja

8 MV 2R 4 MV R When Q amount of heat is given to a gas at constant 3 pressure it performs amount of work The average 3 number of degrees of freedom per molecule of the gas is 1 1 2 4 3 5

Q 5 b A system undergoes a change of state from 1 to 2 along path A during which heat transferred from the system is 40 KJ and the work done on it is 60 KJ Find the change in internal energy of the system If the same system were returned to original state through adiabatic process through path B find the magnitude and direction of work during path B 12 5

At an instant t 0 Block A of mass 1 kg is moving with speed 8 m s towards right on rough surface of block B of mass 3 kg Block B which is placed on smooth horizontal surface is moving with speed 4 m s towards right at same instant t 0 The net work done against the frictional force in long time is block A will not fall from block B A B 8m s 4m s

Given T P curve for three processes Work done in process 1 2 and 3 if initial and final pressure are same for all processes is W W W3 respectively Correct order of arrangement is V P A W W W3 C W W W3 B W W W3 D W W W3

A monoatomic gas y compressed to adiabatically then the pressure of the gas will change to Question Type Single Correct Type 1 24 5 2 8 3 40 3 5 3 is suddenly 1 8 its volume

The state equation V T constant represents A VITRI Options isothermal change R Oiso basic change R Oiso chronic change da O adiabatic change

Q 9 A system is taken through a cyclic process represented by a circle as shown The heat absorbed by the system is V in cc 40 30 20 0 0 H 50 100 150 200 P in kPa J 1 10 J 3 AT Y 10 T 2 4 T 2 TI

2 8 One mole of a gas expands obeying the relation as shown in P V diagram The maximum temperature in this process is equal to 1 PA Por Po 2 PoVo R OR Y 1 A I Vo B 2Vo 2 V 3Po Vo R

18 Neutral gas molecules each of mass m are at a temperature T in a container at zero gravity Ho does the average de Broglie wavelength A of a molecule depend on T A Ax VT B A x 1 T C A x 1 T P x Ti

The ends of metal rod are maintained at temperature 120 C and 150 C The rate of heat flow in the rod is found to be 10 J s If an identical rod is connected in parallel with this rod and ends temperatures are maintained at 220 C and 250 C then net rate of flow of heat will be 1 10 J s 3 30 J s 2 20 J s 4 15 J s 50 20

28 An ideal gas is subjected to cyclic process involving four thermodynamic states the amounts of heat Q and work W involved in each of these states Q 6000 J Q 5500 J Q3 3000 J Q4 3500 J W 2500 J W 1000 J W3 1200 J W x J The ratio of the net work done by the gas to the total heat absorbed by the gas is n The values of x and n respectively are a 500 7 5 2 4 c 1000 21 b 700 10 5 d 1500 15