# 2-PART TEST-1 HEAT & THERMODYNAMICS

STUDY INNOVATIONSEducator en Study Innovations

PART TEST 1 TOPIC : HEAT & THERMODYNAMICS (PHYSICS) GENERAL INSTRUCTIONS 1. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is: (A) 4 R T (B) 5 R T (C) 15 R T (D) 11 R T 2. Maxwell’s velocity distribution curve is given for two different temperatures. For the given curves. (A) T1 > T2 (B) T1 < T2 (C) T1  T2 (D) T1 = T2 3. The ratio of translational and rotational kinetic energies at 100 K temperature is 3 : 2. Then the internal energy of one mole gas at that temperature is[R = 8.3 J/mol-K] (A) 1175J (B) 1037.5 J (C) 2075 J (D) 4150J 4. 12 gm He and 4 gm H2 is filled in a container of volume 20 litre maintained at temperature 300 K. The pressure of the mixture is nearly : (A) 3 atm (B) 5 atm (C) 6.25 atm (D) 12.5 atm 5. Which of the following will have maximum total kinetic energy at temperature 300 K. (A) 1 kg H2 (B) 1 kg He (C) 1 kg H + 2 2 1 kg He (D) 2 1 kg H + 4 2 3 kg He 4 6. A ring shaped tube contains two ideal gases with equal masses and atomic mass numbers M1 = 32 and M2 = 28. The gases are separated by one fixed partition P and another movable conducting partition S which can move freely without friction inside the ring. The angle  as shown in the figure in equilibrium is: 7 (A) 8 15 (C) 16 8 (B) 7 16 (D) 15 7. In an experiment the speeds of any five molecules of an ideal gas are recorded. The experiment is repeated N times where N is very large. The average of recorded values, is : (A) (B) (C) (D) 8. Temperature at which Fahrenheit and Kelvin pair of scales give the same reading will be: (A)  = –40 (B)  = 40 (C)  = 574.25 (D) 512.45 9. 20 gm ice at –10 ºC is mixed with m gm steam at 100 ºC. The minimum value of m so that finally all ice and steam converts into water is : (Use sice=0.5 cal/gmºC,swater =1 cal/gmºC,L (melting)=80 cal/gm and L (vaporization)=540 cal/gm) 185 (A) 27 135 gm (B) 17 gm 85 113 (C) 32 gm (D) 17 gm 10. An ice block at 0°C is dropped from height ‘h’ above the ground. What should be the value of ‘h’ so that it melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice ? [Given : Lf = 80 cal/gm] (A) 33.6 m (B) 33.6 km (C) 8 m (D) 8 km 11. n moles of a gas filled in a container at temperature T is in thermodynamic equilibrium initially. If the gas is compressed slowly and isothermally to half its initial volume the work done by the atmosphere on the piston is: (A) n R T 2 (C) n R T  𝑙 n 2  1 n R T (B)  2 (D)  n R T 𝑙n 2  2 12. In a process the pressure of an ideal gas is proportional to square of the volume of the gas. If the temperature of the gas increases in this process, then work done by this gas: (A) is positive (B) is negative (C) is zero (D) may be positive 13. A vessel contains an ideal monoatomic gas which expands at constant pressure, when heat Q is giv

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### 2-PART TEST-1 HEAT & THERMODYNAMICS

• 1. TOPIC : HEAT & THERMODYNAMICS (PHYSICS) PART TEST __ 1 Duration : 1 Hour Max. Marks : 90 GENERAL INSTRUCTIONS 1. This Question Paper contains 30 objective type questions. 2. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct. 3. For each question, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 1. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is: (A) 4 R T (B) 5 R T (C) 15 R T (D) 11 R T 2. Maxwell’s velocity distribution curve is given for two different temperatures. For the given curves. (A) T1 > T2 (B) T1 < T2 (C) T1  T2 (D) T1 = T2 3. The ratio of translational and rotational kinetic energies at 100 K temperature is 3 : 2. Then the internal energy of one mole gas at that temperature is[R = 8.3 J/mol-K] (A) 1175J (B) 1037.5 J (C) 2075 J (D) 4150J 4. 12 gm He and 4 gm H2 is filled in a container of volume 20 litre maintained at temperature 300 K. The pressure of the mixture is nearly : (A) 3 atm (B) 5 atm (C) 6.25 atm (D) 12.5 atm 5. Which of the following will have maximum total kinetic energy at temperature 300 K. (A) 1 kg H2 (B) 1 kg He (C) 2 1 kg H2 + 2 1 kg He (D) 4 1 kg H2 + 4 3 kg He
• 2. 6. A ring shaped tube contains two ideal gases with equal masses and atomic mass numbers M1 = 32 and M2 = 28. The gases are separated by one fixed partition P and another movable conducting partition S which can move freely without friction inside the ring. The angle  as shown in the figure in equilibrium is: (A) 8 7 (B) 7 8 (C) 16 15 (D) 15 16 7. In an experiment the speeds of any five molecules of an ideal gas are recorded. The experiment is repeated N times where N is very large. The average of recorded values, is : (A) M RT 2 (B) M RT 8  (C) M RT 3 (D) M RT 8. Temperature at which Fahrenheit and Kelvin pair of scales give the same reading will be: (A)  = –40 (B)  = 40 (C)  = 574.25 (D) 512.45 9. 20 gm ice at –10 ºC is mixed with m gm steam at 100 ºC. The minimum value of m so that finally all ice and steam converts into water is : (Use sice=0.5 cal/gmºC,swater =1 cal/gmºC,L (melting)=80 cal/gm and L (vaporization)=540 cal/gm) (A) 27 185 gm (B) 17 135 gm (C) 32 85 gm (D) 17 113 gm 10. An ice block at 0°C is dropped from height ‘h’ above the ground. What should be the value of ‘h’ so that it melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice ? [Given : Lf = 80 cal/gm] (A) 33.6 m (B) 33.6 km (C) 8 m (D) 8 km 11. n moles of a gas filled in a container at temperature T is in thermodynamic equilibrium initially. If the gas is compressed slowly and isothermally to half its initial volume the work done by the atmosphere on the piston is: (A) nRT 2 (B)  nRT 2 (C) n R T n 2 1 2        (D)  n R T n 2 12. In a process the pressure of an ideal gas is proportional to square of the volume of the gas. If the temperature of the gas increases in this process, then work done by this gas: (A) is positive (B) is negative (C) is zero (D) may be positive
• 3. 13. A vessel contains an ideal monoatomic gas which expands at constant pressure, when heat Q is given to it. Then the work done in expansion is: (A) Q (B) 3 5 Q (C) 2 5 Q (D) 2 3 Q 14. 5 moles of Nitrogen gas is enclosed in an adiabatic cylindrical vessel. The piston itself is a rigid light cylindrical container containing 3 moles of Helium gas. There is a heater which gives out a power 100 cal/sec to the nitrogen gas. A power of 30 cal /sec is transferred to Helium through the bottom surface of the piston. The rate of increment of temperature of the nitrogen gas assuming that the piston moves slowly: (A) 2 K/sec (B) 4 K/sec (C) 6 K/sec (D) 8 K/sec 15. The gas law T PV = constant for a given amount of a gas is true for : (A) isothermal change only. (B) adiabatic change only. (C) both isothermal & adiabatic changes. (D) neither isothermal nor adiabatic change. 16. All the rods have same conductance ‘K’ and same area of cross section S. If ends A and C are maintained at temperature 2T0 and T0 respectively then which of the following is/are correct: (A) Rate of heat flow through ABC, AOC and ADC is same (B) Rate of heat flow through BO and OD is not same (C) Total Rate of heat flow from A to C is a 2 T S K 3 0 (D) Temperature at junctions B, O and D are same 17. A hollow copper sphere and a hollow copper cube, of same surface area and negligible thickness, are filled with warm water of same temperature and placed in an enclosure of constant temperature, a few degrees below that of the bodies. Then in the beginning : (A) the rate of energy lost by the sphere is greater than that by the cube (B) the rate of fall of temperature for sphere is greater than that for the cube. (C) the rate of energy lost by the sphere is less than that by the cube (D) the rate of fall of temperature for sphere is less than that for the cube. 18. The colour of a star indicates its : (A) weight (B) size (C) temperature (D) distance
• 4. 19. Two identical solid spheres have the same temperature. One of the sphere is cut into two identical pieces. The intact sphere radiates an energy Q during a given small time interval. During the same interval, the two hemispheres radiate a total energy Q'. The ratio Q'/Q is equal to : (A) 2.0 (B) 4.0 (C) 3 2 (D) 1.5 20. A calorimeter contains 50 g of water at 50°C. The temperature falls to 45°C in 10 minutes. When the calorimeter contains 100 g of water at 50°C, it takes 18 minutes for the temperature to become 45°C. then the water equivalent of the calorimeter is : (A) 12.5 g (B) 6.25 g (C) 25 g (D) 15 g 21. Heat is flowing through two cylindrical rods made of same materials whose ends are maintained at similar temperatures. If diameters of the rods are in ratio 1 : 2 and lengths in ratio 2 : 1, then the ratio of thermal current through them in steady state is : (A) 1 : 8 (B) 1 : 4 (C) 1 : 6 (D) 4 : 1 22. A balloon containing an ideal gas has a volume of 10 litre and temperature of 17ºC. If it is heated slowly to 75ºC, the work done by the gas inside the balloon is (neglect elasticity of the balloon and take atmospheric pressure as 105 Pa) (A) 100 J (B) 200 J (C) 250 J (D) data insufficient 23. In the PV diagram shown. The gas does 5 J of work in isothermal process a b and 4 J in adiabatic process b c. What will be the change in internal energy of the gas in straight path c to a? (A) 9 J (B) 1 J (C) 4 J (D) 5 J 24. A monoatomic ideal gas is filled in a nonconducting container. The gas can be compressed by a movable nonconducting piston. The gas is compressed slowly to 12.5% of its initial volume. The percentage increase in the temperature of the gas is (A) 400% (B) 300% (C) – 87.5% (D) 0% 25. A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until volume is doubled. The average molar heat capacity for whole process is: (A) 6 R 13 (B) 6 R 19 (C) 6 R 23 (D) 6 R 17 26. The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is : (A) 22/7 (B) 21/7 (C) 21/5 (D) 22/5
• 5. 27. Four particles have velocities 1, 0, 2, 3 m/s. The root mean square velocity of the particles is: (in m/s) (A) 3.5 (B) 5 . 3 (C) 1.5 (D) 3 14 28. V–T diagram for a process of a given mass of ideal gas is as shown in the figure. During the process pressure of gas. (A) first increases then decreases (B) continuously decreases (C) continuously increases (D) first decreases then increases. 29. A slab X of thickness ‘t’, thermal conductivity ‘K’and area of cross-section ‘A’ is placed in thermal contact with another slab Y which is 2n2 times thicker,4n times conductive and having n times larger cross section area. If the outside face of X is maintained at 100°C, the outside face of Y at 0°C,then the temperature of the junction  is represented by the graph (n > 0) : (A) (B) (C) (D) 30. Two conducting movable smooth pistons are kept inside a non conducting, adiabatic container with initial positions as shown. Gas is present in the three parts A, B & C having initial pressures as shown. Now the pistons are released. Then the final equilibrium position length of part A will be (A) 8 L (B) 4 L (C) 6 L (D) 5 L
• 6. ANSWER KEY TO PART TEST-1 (PHYSICS) 1. (D) 2. (B) 3. (C) 4. (C) 5. (A) 6. (D) 7. (A) 8. (C) 9. (C) 10. (B) 11. (A) 12. (A) 13. (C) 14. (A) 15. (C) 16. (D) 17. (D) 18. (C) 19. (D) 20. (A) 21. (A) 22. (B) 23. (C) 24. (B) 25. (B) 26. (B) 27. (B) 28. (B) 29. (A) 30. (B)
• 8. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume V0 , in which an ideal gas is contained under the same pressure p0 and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas 2 times compared to that of the other by slowly moving the piston ? (A) p0 V0 (B) 2p0 V0 (C) p0 V0 n 8 9 (D) p0 V0 n2 2. A uniform pressure P is exerted by an external agent on all sides of a solid cube at temperature t ºC. By what amount should the temperature of the cube be raised in order to bring its volume back to its original volume before the pressure was applied if the bulk modulus is B and co-efficient of volumetric expansion is ? (A) P/B (B) P/B (C) B/P (D) 1/BP 3. Two rods of same dimensions, but made of different materials are joined end to end with their free ends being maintained at 100ºC and 0ºC respectively. The temperature of the junction is 70ºC. Then the temperature of the junction if the rods are interchanged will be equal to : (A) 10ºC (B) 30ºC (C) 90ºC (D) 40ºC 4. Assume a sample of an ideal gas in a vessel. Where velocity of molecules are between 2 m/sec to 5 m/sec and velocity of molecules (v) and number of molecules (n) are related as n = 7v – v2 – 10. The most probable velocity in sample is. Where v is measured in m/sec. (A) 3.5 m/sec (B) 5 m/sec (C) 10 m/sec (D) 4 m/sec 5. If specific heat capacity of a substance in solid and liquid state is proportional to temperature of the substance, then if heat is supplied to the solid initially at – 20°C (having melting point 0°C) at constant rate. Then the temperature dependence of substance with time will be best represented by : (A) (B) (C) (D)
• 9. 6. In the figure shown the pressure of the gas in state B is: (A) 25 63 P0 (B) 25 73 P0 (C) 25 48 P0 (D) none of these 7. A hot black body emits the energy at the rate of 16 J m–2 s–1 and its most intense radiation corresponds to 20,000 Å. When the temperature of this body is further increased and its most intense radiation corresponds to 10,000 Å, then the energy radiated in Jm–2 s–1 will be : (A) 4 (B) 1 (C) 64 (D) 256 8. Two identical rectangular rods of metal are welded end to end in series between temperature 0°C and 100°C and 10 J of heat is conducted (in steady state process) through the rod in 2.00 min. If 5 such rods are taken and joined as shown in figure maintaining the same temperature difference betweenAand B, then the time in which 20 J heat will flow through the rods is : (A) 30 sec. (B) 2 min. (C) 3 min. (D) 60 sec. SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. An ideal gas undergoes a cyclic process abcda which is shown by pressure- density curve. P  d a b c 1 2 (A) Work done by the gas in the process 'bc' is zero (B) Work done by the gas in the process 'cd' is negative (C) Internal energy of the gas at point 'a' is greater than at state 'c' (D) Net work done by the gas in the cycle is negative. 10. The emissive power of a black body at T = 300 K is 100 Watt/m2 . Consider a body B of area A = 10 m2 coefficient of reflectivity r = 0.3 and coefficient of transmission t = 0.5 and at temperature 300 K. Then which of the following is correct : (A) The emissive power of B is 20 W/m2 (B) The emissive power of B is 200 W/m2 (C) The power emitted by B is 200 Watts (D) The emissivity of B is = 0.2 11. The ends of a rod of uniform thermal conductivity are maintained at different (constant) temperatures. After the steady state is achieved : (A) heat flows in the rod from high temperature to low temperature even if the rod has nonuniform cross sectional area. (B) temperature gradient along length is same even if the rod has non uniform cross sectional area. (C) heat current is same even if the rod has non-uniform cross sectional area. (D) if the rod has uniform cross sectional area the temperature is same at all points of the rod.
• 10. 12. Number of collisions of molecules of a gas on the wall of a container per m2 will : (A) Increase if temperature and volume both are doubled. (B) Increase if temperature and volume both are halved. (C) Increase if pressure and temperature both are doubled. (D) Increase if pressure and temperature both are halved. SECTION - III Reasoning Type This section contains 4 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statement -1 : It is possible for both the pressure and volume of a monoatomic ideal gas of a given amount to change simultaneously without causing the internal energy of the gas to change. Statement-2: The internal energy of an ideal gas of a given amount remains constant if temperature does not change. It is possible to have a process in which pressure and volume are changed such that temperature remains constant. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 14. Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures. Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant. (A) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 15. Statement-1 : Burns sustained from steam at 100o C are usually more serious than those sustained by boiling water (at 100o C) Statement-2 : To convert 1gm of water at 100o C to 1 gm of steam at 100o C, 540 calories of heat is to be supplied. Hence 1gm of steam at 100o C has more heat content than 1 gm of water at 100o C (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 16. Statement-1 : If the absolute temperature of a gas is doubled, the final rms-velocity of the gas particles becomes 2 times the initial value. Statement-2: The average translational kinetic energy of molecules in a gas is equal to both 2 1 mvrms 2 and 2 3 kT.( where vrms , k and T have usual meanings) (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.
• 11. SECTION - IV Comprehension Type This section contains 2 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 17 to 19 A 0.60 kg sample of water and a sample of ice are placed in two compartmentsA and B that are separated by a conducting wall, in a thermally insulated container. The rate of heat transfer from the water to the ice through the conducting wall is constant P, until thermal equilibrium is reached. The temperature T of the liquid water and the ice are given in graph as functions of time t. Temperature of the each compartment remain homogeneous during whole heat transfer process. Given specific heat of ice = 2100 J/kg-K Given specific heat of water = 4200 J/kg-K Latent heat of fusion of ice = 3.3 × 105 J/kg 17. The value of rate P is (A) 42.0 W (B) 36.0 W (C) 21.0 W (D) 18.0 W 18. The initial mass of the ice in the container is equal to (A) 0.36 kg (B) 1.2 kg (C) 2.4 kg (D) 3.6 kg 19. The massof the ice formed due to conversion from the water till thermal equilibrium isreached, isequal to (A) 0.12 kg (B) 0.15 kg (C) 0.25 kg (D) 0.40 kg
• 12. Paragraph for Question Nos. 20 to 22 A quantity of an ideal monoatomic gas consists of n moles initially at temperature T1. The pressure and volume both are then slowly doubled in such a manner so as to trace out a straight line on a P-V diagram. 20. For this process, the ratio 1 nRT W is equal to (where W is work done by the gas) : (A) 1.5 (B) 3 (C) 4.5 (D) 6 21. For the same process, the ratio 1 nRT Q is equal to (where Q is heat supplied to the gas) : (A) 1.5 (B) 3 (C) 4.5 (D) 6 22. If C is defined as the average molar specific heat for the process then R C has value (A) 1.5 (B) 2 (C) 3 (D) 6 SECTION - V Matrix - Match Type This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column-I and five statements (p,q,r, s and t) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t. 23. A sample of gas goes from state A to state B in four different manners, as shown by the graphs. Let W be the work done by the gas and U be change in internal energy along the path AB. Correctly match the graphs with the statements provided. Column  Column  (A) (p) W is positive (B) P T A B (q) U is negative
• 13. (C) (r) W is negative (D) (s) U is positive States A and B are very close (t) heat rejected Q < 0 24. A copper rod (initially at room temperature 20°C) of non-uniform cross section is placed between a steam chamber at 100°C and ice-water chamber at 0°C. Column  Column  (A) Initially rate of heat flow       dt dQ will be (p) maximum at section A (B) At steady state rate of heat flow       dt dQ will be (q) maximum at section B (C) At steady state temperature gradient       dx dT will be (r) minimum at section C (D) At steady state rate of change of (s) minimum at section B temperature       dt dT at a certain point will be (t) same for all section
• 14. ANSWER KEY TO PART TEST-2 PHYSICS 1. (C) 2. (B) 3. (B) 4. (A) 5. (C) 6. (B) 7. (D) 8. (D) 9. (A)(B)(D) 10. (A)(C)(D) 11. (A)(C) 12. (B)(C) 13. (A) 14. (A) 15. (A) 16. (A) 17. (A) 18. (C) 19. (B) 20. (A) 21. (D) 22. (B) 23. (A) r,s,t (B) q,r,t ; (C) p, q, t (D) p 24. (A) p, r , (B) t (C) q , r (D) t