Title 7-gaseous-state--thermodynamics-.pdf ✅

9. A gaseous mixture consists of 2 moles of O2 and 4 moles of Ar at a temperature T. Neglecting all vibrational moles, the total internal energy of the system is (A) 4RT (B) 15RT (C) 9RT (D) 11RT 10. Figure shows two processes A and B in a system. Let ΔQ1 and ΔQ2 be heat given to the system in processes A and B, respectively, then (A) ΔQA > ΔQB (B) ΔQA = ΔQB (C) ΔQA < ΔQB (D) ΔQA ≤ ΔQB 11. The pressure and density of a diatomic gas (γ = 7/5) change adiabatically from (P, ρ ) to ( P ′ , ρ ′ ). If ρ ′ /ρ = 32, then P ′ /P should be: (A) 1/128 (B) 128 (C) 32 (D) None 12. The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is U = a + bPV where a and b are constants. What is the value of the ratio of the specific heats ? (A) a b (B) b+1 b (C) α+1 α (D) b α 13. In the figure, the gas does 5 J of work along isothermal process ab and 4 joule of work along adiabatic process bc. Then the change in the internal energy of the gas if the gas follows the straight path from a to c is : (A) 9 J (B) − 9 J (C) − 4 J (D) None of these 14. The velocity of sound in a gas at NTP is 0.68 times the rms velocity of the gas molecule at NTP. The number of degrees of freedom of the molecules is : (A) 5 (B) 6 (C) 3 (D) 4 15. A cylinder made of perfectly conducting material closed at both ends is divided into two equal parts by a heat proof piston. Both parts of the cylinder contain the same masses of a gas at a temperature t0 = 27∘ and pressure P0 = 1 atm. Now if the gas in one of the parts is slowly heated to t = 57∘C, the distance moved by the piston from the middle of the cylinder will be (length of the cylinder = 84 cm ) (A) 3 cm (B) 5 cm (C) 2 cm (D) 1 cm MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. Two gases have the same initial pressure, volume and temperature. They expand to the same final volume, one adiabatically and the other isothermal. (A) the final temperature is greater for the isothermal process (B) the final pressure is greater for the isothermal process (C) the work done by the gas is greater for the isothermal process. (D) all the above options are incorrect 17. The molar heat capacity for an ideal gas (A) is zero for an adiabatic process (B) is infinite for an isothermal process (C) depends only on the nature of the gas for a process in which either volume or pressure is constant
(D) is equal to the product of the molecular weight and specific heat capacity for any process 18. A system undergoes a cyclic process in which it absorbs heat, Q1 and gives out heat, Q2. The efficiency of the process is η and the work done is W. (A) W = Q1 − Q2 (B) η = W Q1 (C) η = Q2 Q1 (d) η = 1 − Q2 Q1 19. An ideal gas is taken from the state A (pressure P, volume V ) to the state B (pressure P/2, volume 2 V ) along a straight line path in the P − V diagram. Select the correct statement (s) from the following (A) The work done by the gas in the process A to B exceeds the work that would be done by it, if the system were taken from A to B along the isotherm. (B) In the T − V diagram, the path AB becomes a part of parabola. (C) In the P-T diagram, the path AB becomes a hyperbola. (D) In going from A to B, then temperature T of the gas first increase maximum value and then decrease. 20. Two adiabatic processes bc and ad for the same gas are given to intersect two isotherms at T1 and T2 (as shown). Then (A) Va Vb = T2 T1 (B) Va Vd = T1 T2 (C) Vb Vc = ( T2 T1 ) 1 γ−1 (D) VaVc = VbVd 21. The diagram shown depicts three different states 1,2&3 for an ideal gas. It is also known that temperatures at states (1) & (2) are same. Then: (A) 1 → 2 is an isothermal expansion process (B) 1 → 3 is an expansion process and is accompanied by cooling (C) 3 → 2 is an expansion process accompanied by cooling (D) internal energy must increase in process 1 → 3 22. 2 moles of He are mixed with 2 moles of H2 in a closed adiabatic container. Initially the mixture occupies 3 liters at 27∘C. The volume is suddenly decreased to ( 3 2 ) liters. Choose the correct option(s) (H2 and He can be treated as ideal gases) : (A) γ for mixture is 3 2 (B) final temperature = 300√2 K (C) CP for mixture is 2R (D) Work done in compression is totally converted into internal energy 23. A closed container is fully insulated from outside. One half of it is filled with an ideal gas X separated by a plate P from the other half Y which contains a vacuum as shown in figure. When P is removed, X moves into Y. Which of the following statements is correct? (A) No work is done by X (B) X decreases in temperature (C) X increases in internal energy (D) X pressure becomes half