Thermodynamics Questions and Answers

20 An ideal gas is trapped in a thin glass tube of cross section area between two metallic pistons that can slide without friction Initially th pistons stay in equilibrium a distance d apart that is small compared their diameter If the pistons are given unlike charges each of modulu q what will the distance between them become Electrical permittivi of the gas is and atmospheric pressure is po 22o A d 2 EnRA 9 2

If the intermolecular forces vanish away the volume occupied by the molecules contained in 4 5 kg water at standard temperature and pressure will be 1 5 6 m 2 4 5 m 3 11 2 litre 4 11 2 m 3

16 A gas enclosed in a chamber passes through the cycle as shown Determine the net heat added to the system during process CA if the heat QAB added during process AB 20 0 J No heat is transferred during process BC and the net work done during the cycle is 15 0 J 1 5 J 3 20 J o Pressure Nm Volume m 2 OJ 4 5 J

14 An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units Which of the following values of final pressure and volume corresponds to an isothermal change 1 12 1 2 6 2 3 4 3 4 All of these

Shafts A and B connect the gear box to the wheel assemblies of a tractor and shaft C connects it to the engine Shafts A and B lie in the vertical yz plane while shaft C is directed along the x axis Replace the couples applied to the shafts by a single equivalent couple specifying its magnitude and the direction of its axis 20 1200 lb ft 120 900 lb ft 840 lb ft B

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir The entropy change of the universe is 1 equal to entropy change of the reservoir 2 equal to entropy change of water 3 equal to zero 4 always positive

Temperature of a 5 mole of hydrogen gas decreases by 260K while expanded through adiabatic process What is the change in internal energy of the gas 1 1350 J 2 1350 J 3 O 4 250 J How much he

A tank of carbon dioxide at room temperature and pressurized to 60 atm is used to make dry ice solid carbon dioxide based on the cooling provided by the adiabatic expansion of the gas when it is released from the tank If they factor for carbon dioxide is 5 3 what will be the final temperature of the expanded gas

Example 6 Given Avogadro s number N 6 02 x 1023 and Boltzmann s constant k 1 38 10 23 J K a Calculate the average kinetic energy of translation of the molecules of an ideal gas at 0 C and at 100 C b Also calculate the corresponding energies per mole of the gas Solution a According to the kinetic theory the averago kinatio 90014

A reversible heat engine receives 2 kJ of heat from a reservoir at 1000 K and a certain amount of heat from a reservoir at 800 K It rejects 1 kJ of heat to a reservoir at 400 K The net work output in kJ of the cycle is 1 0 8 2 1 0 3 1 4 4 2 0

What amount of heat in J is to be transferred to nitrogen in the isobaric heating process for the gas to perform the work of 2 0J fy af fod 2 0

A gaseous mixture consists of 20 g of hellum and 32 g of oxygen The ratio 0 12 1 6 02 1 0 28 for the mixture is 100 21 26 31 36 41 46 51 56 61 66 71 76

A Carnot engine receives 2 0 kJ of heat from a reservoir at 500 K does some work and rejects some heat to a reservoir at 350 K a How much work does it do b How much heat is rejected c What is its efficiency

A man of mass m stands on a crate of mass M He pulls on a light rope passing over a smooth light pulley The other end of the rope is attached to the crate For the system to be in equilibrium the force exerted by the man on the rope will be 1 M m g 2 M m g 3 Mg M 4 mg

A heat engine operates between a high temperature reservoir at 610 K and a low temperature reservoir at 320 K In one cycle the engine absorbs 6400 J of heat from the high temperature reservoir and does 2200 J of work What is the net change in entropy as a result of this cycle 6 5 J K 3 J K 2 6 J K 6 J K

a How much heat is required to convert 7 5 kg of ice from a temperature of 12 C to water vapor at a temperature of 200 F b You have 200 g of coffee at 45 C Coffee has the same specific heat as water How much 3 C ice do you need to add to reduce the coffee s temperature to 30 C

The amount of heat energy required to raise the temperature of Ig of Helium at NTP from T K to T K is T 1 NK T T 3 2 N K T T 3 T N ka 4 N k T T NEET 2013 portional to the cube of its temperature The ration

A thermally insulated piston divides a container into two compartments Volume temperature and pressure in the right compartment are 2V T and 2P while in the left compartment the respective values are V T and P If the piston can slide freely then in the final equilibrium position the volume of the right hand compartment will be 1 V 12V 5 2 3 5 3V 9V 3 1 4

A heat engine operating between a hot reservoir at 600 K and a cold reservoir at 200 K has an efficiency that is 70 of its maximum possible value If it receives 1x10 5 J heat energy from the hot reservoir in 25 minutes it can do a quantity of work equal to 0 A 3 0 X10 5J O B 4 2X10 5J O C 2 2X10 5J 2 DEY

A diffuser has air entering at 100 kPa 300 K with a velocity of 200 m s The inlet cross sectional area of the diffuser is 100 mm At the exit the area is 860 mm and the exit velocity is 20 m s Determine the exit pressure and temperature of the air P 123 92 kPa T 319 74 K

2 For liquid water the isothermal compressibility is given by K V P b where c b are functions of temperature only If 1 kg of water is compressed isothermally reversibly from 1 to 500 bars at 333K how much work is required At 333K b 2700 bar c 0 125 cm g 0 516 J gm

A rigid and insulated tank of 2 m capacity is divided into two equal compartments by a partition One compartment contains an ideal gas at 600 K and 1 MPa while the second compartment contains the same gas at 300 K and 0 1 MPa Determine the final temperature and pressure of the gas in the tank if the partition gets punctured Assume y 1 4 for the gas T 550 K P 0 55 MPa A 10 m high cylinder cross sectional area 0 1 m has a mass less piston at the bottom with water at 20 C on top of it shown in figure below Air at 300 K volume 0 3 m under the piston is heated so

4 An ideal gas heat engine operate between 27 C and 127 C If it absorbs 10 kcal per cycle at higher temperature then amount of heat energy thrown to sink per cycle is 1 2 5 kcal 3 5 kcal 2 7 5 kcal 4 8 5 kcal

An ideal gas expands from initial volume V to final volume V in two ways viz slowly and quickly re Then 1 Final pressure of quicker expansion is more than that of slower expansion 2 Work output in quicker expansion is more than slower expansion 3 Pressure change is more in quicker expansion than that in slower 4 Pressure change is more in slower expansion than that in quick

10 300 c 0 125 cm g 0 516 J gm 3 Calculate the reversible work done in compressing 0 0283 m of mercury at a constant and temperature of 0 C from 1 atm to 3000 atm The isothermal compressibility of mercury at 0 C is K 3 9 x 10 0 1 x 10 P where P is in atm and k is in atm 0 52J 4 A substance for which I is a constant undergoes an isothermal mechanically reversible process

A large chunk of ice at 0 C is thrown into lake Ontario at 15 C Heat flows from the lake into the ice until to melt it While it is melting the ice s temperature remains at 0 C similarly the lake is so large that its temperature remains at 15 C a For the ice is the heat transfer Qice positive or negative b For the lake is the heat transfer Qlake positive or negative c Which is larger Qice or Qlake or are they the same Consider the absolute values only Explain your answer d Is the entropy change of the ice ASice positive or negative e Is the entropy change of the lake ASlake positive or negative f Which is larger ASice or ASlake or are they the same Consider the absolute values only Explain your answer

Express the volume expansivity and the isothermal compressibility as functions of density p and its partial derivatives For water at 323K 50 C and 1 bar k 44 18x10 bar To what pressure must water be compressed at 323 K 50 C to change its density by 1 Assume that k is independent of P 226 2 bar

ays positive J K CET gas is changed of the following 1 P V T V JIPMER mal energy and e system then 46 The four curves A A2 A3 and 44 are shown on PV diagram Which of the curves represents adiabatic process a A3 A4 A3 b A4 A A c A V d A AMiL Med

Liquid water at 25 C and I bar fills a rigid vessel If heat is added to the water until its temperature reaches 50 C what pressure is developed The average value of between 25 and 50 C is 36 2 x 10 K The value of x at 1 bar and 50 C is 4 42 x 10 bar and may be assumed independent of P The specific volume of liquid water at 25 C is 1 0030 cm g 206 barl

A thermally insulated chamber of volume 2V0 is divided by a frictionless insulating piston of area S into two equal parts A and B Part A has an ideal gas at pressure Po and temperature To and in part B is vacuum A massless spring of force constant K is connected with the piston and the wall of the container as shown Initially the spring is unstretched The ideal gas in chamber A is allowed to expand Let in equilibrium the spring be compressed by a length xo then Final pressure of the gas is Kx S Work done by the gas is tox D Magnitude of change in internal energy of the gas is kx 1 2 Temperature of the gas in equilibrium is less than initial temperature A B mooooo

The given indicator diagram shows variation of pressure with volume when a thermodynamical system is taken from state A to state B During the process PA A B V 0 0 1 The system is cooled 2 The system is heated 3 The system heated first and then cooled 4 The system cooled first and then heated

57 When a monochromatic point source of light is at a distance r from a photoelectric cell the cut off voltage is V and the saturation current is I If the same source is placed at a distance 3r away from the photoelectric cell then a the saturation current will not change b the saturation current will change to I 9 c the stopping potential will not change d the stopping potential will increase to 3 V hotoelectric effect the

MPLE 13 The cylinder shown in the figure has conducting walls and temperature of the surrounding is T the pistion is initially in equilibrium the cylinder contains n moles of a gas Now the piston is displaced slowly by an external agent to make the volume double of the initial Find work done by external agent in terms of n R T n moles

The efficiency of a Carnot engine at a particular source and sink temperature is When the sink temperature is reduced by 50 C the engine efficiency becomes Source temperature should be 300 K 150 K 600 K 100 K 2 WIN

A body of mass 5 kg falls from a height 30 metre If its all mechanical energy is change into heat then heat produced will be 2 150 cal 1 350 cal E 3 60 cal 4 6 cal

4 increase the sensitivity 3 increase the moment of inertia According to Newton s law of cooling the rate of cooling of a body is proportional to AO where A is the difference in temperature of the body and its surroundings Value of nis 1 Two 2 Three 3 Four 4 One

One mole of an ideal gas is taken from state P to state Q by three different processes 1 PRQ II PSQ and III PTQ as shown in the figure The heat absorbed by the gas is P R S P T More in process II than in process I Minimum in the process II Same in process I and in process III More in process II than in process III

A hot body at temperature T losses heat to the surrounding temperature Ts by radiation If the difference in the temperature is small then the rate of loss of heat by the hot body is proportional to a T Ts b T Ts c d T Ts J K CET T T 2

One mole of ideal gas undergoes cyclic process shown in figure Process 12 is adiabatic Heat given to gas in the process is nearly A Q W DU 2 63 piloo V Vo 10 1 59 J 3 42 I 3 290 K T 2 47 J 4 None of these

The ratio Cp Y for an ideal gas Its molecular weight is M Its specific heat capacity at constant pressure is Cv R Y 1 YR Y 1 YR M y 1

A cubical container having each side as is filled with a gas having N molecules in the container Mass of each molecule is m If we assume that at every instant half of the molecules are moving towards the positive x axis and half of the molecules are moving towards the negative x axis Two walls of the container are perpendicular to the x axis Find the net force acting on the two walls given Assume that all the molecules are moving with speed vo

Exam 15 13 A thermodynamical 3 A m C process is shown in figure with PA 3 10 Pa V 2 10 PB 8 x 104 Pa Vc 5 x 10 m In the processes AB and BC 600 J and 200 J of heat is added to the system respectively Find the change in internal energy of the system in process AC pt B A C V

A cylindrical vessel with a massless movable piston of area of cross section 0 1 m contains an ideal gas The piston is connected to an ideal spring of spring constant 106 N m Initially the spring is compressed by 2 cm Now heat is supplied to the vessel until the compression in the spring has increased to 5 cm The work done by the gas during the process is kJ Atmospheric pressure 1 www 10 Pa

46 An ideal monoatomic gas undergoes a cyclic process shown by following P V diagram The dotted curves are isotherms The efficiency of a heat engine based on this process is 4000K 1 3 152 2 13 P 2000K A 1000K corp B C 2 4 IN MI

round the reversible rectangular cycle ABCDA as shown in the diagram The temperature at A is To B 2Po P Po A To C D Vo 2V0 V The thermodynamic efficiency of the cycle is a 15 b 50 c 20 d 25 2004

A thermodynamic system is taken from an initial state i with internal energy U 100 J to the final state f along two different paths iaf and ibf as schematically shown in the figure The work done by the system along the paths af ib and bf are Waf 200 J Wib 50 J and Wbf 100 J respectively The heat supplied to the system along the path iaf ib and bf are Qiaf Qbf and Qib respectively If the P a b V internal energy of the system in the state b is Ub 200 J and 500 I the rati

5 The volume of a gas reduced to one third of its original volume slowly Calculate the final pressure if the initial pressure is 4 atmospheric Ans 12 atmospheric 5 In the above question if the process has taken place suddenly then calculate the final pressure y for the given gas 1 5 Ans 12 3 atmospheres In the question No 6 if the initial temperature is 30 C then calculate the final temp Ans 51 96 C

7 Water at 20 C is poured into a test tube whose bottom is immersed in a large amount of water at 80 C As a result the water in the test tube is heated to 80 C during a time t Then water at 80 C is poured into the test tube whose bottom is immersed in a large amount of water at 20 C The water in the test tube is cooled to 20 C during a time t What time is longer t or t

88 On a pT diagram a cyclic process is performed as shown Where is the volume maximum a a P b b a ck b d c c T d d

Figure 26 E5 1 A gas is taken through a cyclic process ABCA as sh in figure 26 E6 If 2 4 cal of heat is given in the pro what is the value of J