Tiêu đề 13. Thermodynamics hard.pdf ✅

1. Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of n moles having pressure Po, volume Vo and temperature To is (a) (b) (c) (d) 2. A ball of surface temperature T is in thermal equilibrium with its environment of constant temperature. Which of the curves in figure gives the energy E radiated by the sphere versus time t: (a) 1 (b) 2 (c) 3 (d) 4 3. At pressure P and absolute temperature T a mass M of an ideal gas fills a closed container of volume V. An additional mass 2M of the same gas is added into the container and the volume is then reduced to and the temperature to The pressure of the gas will now be: (a) (b) P (c) 3 P (d) 9 P 4. If HC, HK and HF are heat required to raise the temperature of one gram of water by one degree in Celsius, Kelvin and Fahrenheit temperature scales respectively then : (a) HK> HC> HF (b) HF> HC> HK (c) HK=HC>HF (d) HK=HC = HF 5. A certain gas is taken to the five states 1, 2, 3, 4 and 5 represented by dots in PV in graph. The plotted curves are isotherms. Order of the most probable speed vmpof the molecules at these five states is : (a) Vmp at 3>Vmp at 1= Vmp at 2>Vmp at 4 =Vmp at 5 (b) Vmp at 1 >Vmp at 2 =Vmp at 3 >Vmp at 4 >Vmp at 5 (c) Vmp at 3>Vmp at 2 = Vmp at 4 >Vmp at 1 >Vmp at 5 (d) Vmp at 3 >Vmp at 2 >Vmp at 4 >Vmp at 1 >Vmp at 5 6. For a gas sample with N number of molecules, function N(v) is given by N(V)= V2 for 0 < V < V0 and N (V) = 0 for V > Vo. Where dN is number of molecules in speed range V to V + dV. The rms speed of molecules is : (a) Vo (b) Vo (c) Vo (d) Vo 7. Heat is I. Transfer of energy without performing work. II. Energy in transit. III. Always transferred from higher temperature to lower temperature. Incorrect statement is: (a) I (b) II (c) III (d) None 8. For a real gas, the force of interaction between molecules of a gas is different from force of interaction between molecules of the walls of the container and gas molecules (both gas and the container are in thermodynamic equilibrium). This indicates that: (a) Pressure near the walls of the container is different from pressure inside the bulk of the gas but distribution of the molecules inside the container is uniform. (b) Pressure is uniform throughout the container but distribution of the molecules is different for two regions. (c) Both pressure and distribution of molecules is uniform throughout the container. (d) Both pressure and distribution of molecules is different for the two regions. 9. Corresponding to the behaviour of the molecules of an ideal gas, which of the following statement is incorrect? (a) A molecule may loose some part of its kinetic energy when it collides elastically with another molecule. (b) There is a potential energy associated with the interaction between the molecules. (c) Collisions between the molecules of a gas sample cannot change the internal energy of the gas sample. (d) The speed of a molecule is not changed after collision with a wall of the container that is in thermodynamic equilibrium with the gas. 10. Three objects of different materials but of equal masses are kept in a heating chamber where all three receive energy at a same constant rate. During heating each object starts with liquid state and finally gets converted in the gaseous state. For each of the object, temperature T versus time t graph is plotted, as shown and marked I, II and III. II. If Ll, Lll and Llll represent their respective latent heat of vapourization then (a) Llll>Lll>L (b) Ll>Llll>Lll (c) LII> LIII> LI (d) LII> LI> LIII 11. Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. The piston A is free
to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30K, then the rise in temperature of the gas in B is. (a) 30K (b) 18K (c) 50K (d) 42K 12. The temperature of an ideal gas is increased for 100k to 400k. If at 100k the root mean square velocity of the gas molecules is v, at 400k it becomes (a) 4v (b) 2Vb (c) v/2 (d) v/4 13. At room temperature the rms speed of the molecules of a certain diatomic gas is found to be 1930 m/s the gas is (a) H2 (b) F2 (c) O2 (d) Cl 2 14. A black body is at a temperature of 2880K. The energy of radiation emitted by this object with wave length between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. Wein constant b=2.88 x 106 nmK. Then (a) U1 = 0 (b) U3 = 0 (c) U1 = U2 (d) U2> U1 15. Gas at pressure Po is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal to Gas at pressure Po is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal to Gas at pressure Po is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal t (a) 2Po (b) Po/4 (c) Po (d) Po/2 16. When an ideal diatomic gas is heated at constant pressure than the ratio of heat energy given to the change in internal energy of the gas is (a) 7/5 (b) 5/7 (c) 3/5 (d) 5/3 17. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is: (a) 2/5 (b) 3/5 (c) 3/7 (d) 5/7 18. Two mole of argon are mixed with one mole of hydrogen, then Cp/Cv for the mixture is nearly (a) 1.2 (b) 1.3 (c) 1.4 (d) 1.5 19. Two insulting cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at temperature 300K. The piston A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30K. Then the rise in temperature of the gas in B is. (a) 30K (b) 18K (c) 50K (d) 42K 20. Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of gas contained in A is mA and that in B is mB . The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The change in the pressure in A and B are found to be P and 1.5 P respectively. Then (a) 4 mA = 9 mB (b) 2 mA = 3 mB (c) 3 mA = 2 mB (d) 9 mA = 4 mB 21. The average translational energy and the rms speed of molecules in a sample of oxygen at 300K are 6.21 x 10-21J and 484 m/s respectively. The corresponding values at 600K are nearly (assuming ideal gas behavior). (a) 12.42 x 10-21J, 968 m/s. (c) 6.21 x 10-21J, 968 m/s (b) 8.78 x 10-21J, 684m/s (d) 12.42 x 10-21J, 684 m/s 22. In a room where the temperature is 30oC, a body cools from 61oC to 59oC is 4 minutes. The time taken by the body to cool from 51oC to 49oC will be: (a) 4 minutes (b) 6 minutes (c) 5 minutes (d) 8 minutes 23. A monoatomic gas (r = 5/3) is suddenly compressed to th 8 1       its volume adiabatically. The pressure of the gas will changes to (a) 5 24 (b) 8 (c) 3 40 (d) 32 24. Two rods of length 1 and2 are made of materials whose coefficients of linear expansion are 1 and2. If the difference between two lengths is independent of temperature then, (a) 2 α 1 α 2 1 =   (b) 1 2 α α 2 1 =   (c) 2 α 2 1 1 α 2 2  = (d) 2 2 2 α 1 2 1 α   = 25. The volume of a gas at constant pressure of 103 N/m2 expands by 0.25 m3 . The work done by gas is equal to (a) 2.3 erg. (b) 250J (c) 250W (d) 250N 26. P – V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to 1 2 V P (a) He and O2 (b) O2 and He (c) He and Ar (d)O2 and N2
27. Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0 0C and 900C respectively. The temperature of the junction of the three rods will be 900C 900C 0 0C (a) 450C (b) 600C (c) 300C (d) 200C 28. The pressure and volume of a given mass of gas at a given temperature are P and V respectively. Keeping temperature constant, the pressure is increased by 10% and then decreased by 10%. The volume how will be - (a) Less than V (b) More than V (c) Equal to V (d) Less than V for diatomic and more than V for monoatomic 29. A mass of an ideal gas of volume V at pressure P undergoes the cycle of changes shown in the graph – At which point is the gas coolest and hottest ? X Z Y V/10–4m 3 1 5 1 4 P/105Nm–2 Coolest hottest (a) X Y (b) Y X (c) Y Z (d) Z Y 30. An ideal gas is expanded so that amount of heat given is equal to the decrease in internal energy. The gas undergoes the process TV1/5 = constant. The adiabatic compressibility of gas when pressure is P, is – (a) 5P 7 (b) 7P 5 (c) 5P 2 (d) 3P 7 31. A mixture of 8gm of helium and 14gm of nitrogen is enclosed in a vessel of constant volume at 300K. The quantity of heat absorbed by the mixture to double the root mean velocity of its molecules is –(R = universal gas constant ) (a) 2725 R (b) 3630 R (c) 3825 R (d) 5625 R 32. P-T graph of ideal monoatomic gas is given as shown in figure. The corresponding P-V diagram is 2 3 4 1 T P (a) 2 3 1 4 V P (b) 2 3 1 4 V P (c) 2 3 1 4 V P (d) V P 3 2 4 1 33. An expansion process on a diatomic ideal gas (Cv = 5/2 R), has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are : the pressure is 300 kPa, the volume is 0.08 m3 and the temperature is 390 K. The final pressure is 90kPa and the final temperature is 320 K. The change in the internal energy of the gas, in SI units, is closest to: (a) –11, 000 (b) –6500 (c) 11, 000 (d) Zero 34. In Figure, an ideal gas is carried around the cyclic process. How much work is done in one cycle if P0 = 8atm and V0 = 7.00 liters. P0 V0 2P0 P V 2V0 (a) 5656 J (b) –5656 J (c) 10,600 J (d) 11,300 J 35. Which of the following is a FALSE statement? (a) Heat is energy transferred into or out of a system as a result of a temperature difference between the system and its surroundings. (b) The heat added to an ideal gas during the transition from state 1 to state 2 depends only on the initial and final states, 1 and 2, and not on the path by which the gas went from one to the other. (c) When a gas goes from one state to another, the work done depends on the path followed (d) It does not make sense to refer to "the amount of heat in a body". 36. An ideal mono-atomic gas undergoes a cyclic process ABCA as shown in the figure. The ratio of heat absorbed during AB to the work done on the gas during BC is –
B C A 2V0 V0 T0 2T0 V T (a) 2ln 2 5 (b) 3 5 (c) 4ln 2 5 (d) 6 5 37. An ideal gas is taken through the cycle A → B → C →A , as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process C → A is – C 10 A B P(N/m2 ) 2 1 V(m3 ) (a) –5 J (b) – 10 J (c) – 15 J (d) – 20 J 38. The equation of process of a diatomic gas is P 2 =  2V, where  is a constant. Then choose the correct option- (a) Work done by gas for a temperature change T is 3 2 nRT (b) The change in internal energy is 2 5 nRT for a temperature change T (c) Specific heat for the process is 9 19 R (d) The change in internal energy for a temperature change T is 2 5 nRT 39. The curves shown represent adiabatic curves for monoatomic, diatomic &polyatomic( = 4/3) gases. The slopes for curves 1,2,3 respectively at point A are – 1 2 3 P P A T T (a)2.5 T P , 3. 5 T P , 4.5 T P (b) 2.5 T P , 3 T P , 4 T P (c)2.5 T P , 3.5 T P , 4 T P (d) 4 T P , 3.5 T P , 2.5 T P 40. Area of piston is 1 m2 . When heat is supplied to the gas it expands and displaces piston by 2 L where L = 1m. Natural length of springs is L = 1m. Spring constant K = 100 N/m. The pressure of gas in final situation is – gas K Vacuum K L L (a) 50 N/m2 (b) 100 N/m2 (c) 200 N/m2 (d) 400 N/m2 41. The internal energy of a diatomic gas is given as U = U0V, where U0 is a constant. Molar heat capacity of gas is - (a) 2 5 R (b) 2 7 R (c) 2 9 R (d) 2 3 R 42. For an ideal gas graph is shown for three processes. Processes 1, 2, and 3 are respectively – 3 2 T Temperatrue change work done (magnitude) 1 (a) Isochoric, isobaric, adiabatic (b) Isochoric, adiabatic, isobaric (c) Isobaric, adiabatic, isochoric (d) Adiabatic, isobaric, isochoric 43. Two moles of monoatomic gas is mixed with one mole of diatomic gas at the same temperature. Molar heat capacity at constant volume for the mixture is - (a) 6 13R (b) 6 11R (c) 3 5R (d) 6 7R 44. The figure shows two isotherms at temperatures T1 and T2. A gas is taken from one isotherm to another isotherm through different processes. Then change in internal energy U has relation - P e a T2 T1 b c d V (a) Uab>Uac>Uad>Uae (b) Uab = Uac>Uad>Uae (c) Uab = Uac = Uad = Uae (d) Uab<Uac<Uad<Uae 45. An ideal gas whose adiabatic exponent is is expanded so that the amount of heat transferred to the gas is equal to the decrease