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12.THERMODYNAMICS (1.)A Carnot engine has efficiency 1/5. Efficiency becomes 1/3 when temperature of sink is decreased by 50K. What is the temperature of sink? (a.) 325 K (b.) 375 K (c.) 300 K (d.) 350 K (2.)A refrigerator absorbs 2000 cals of heat from ice trays. If the coefficient of performance is 4, then work done by the motor is (a.) 2100 J (b.) 4200 J (c.) 8400 J (d.) 500 J (3.)When the amount of work done is 333 cal and change in internal energy is 167 cal, then the heat supplied is (a.) 166 cal (b.) 333 cal (c.) 500 cal (d.) 400 cal (4.)Carnot cycle (reversible) of a gas represented by a Pressure-Volume curve is shown in the diagram Consider the following statements I. Area ABCD = Work done on the gas II. Area ABCD = Net heat absorbed III. Change in the internal energy in cycle = 0 Which of these are correct (a.) I only (b.) II only (c.) II and III (d.) I, II and III (5.)An ideal gas is heated at constant pressure and absorbs amount of heat Q. If the adiabatic exponent is γ, then the fraction of heat absorbed in raising the internal energy and performing the work, in (a.) 1 − 1 γ (b.) 1 + 1 γ (c.) 1 − 2 γ (d.) 1 + 2 γ (6.)For an adiabatic expansion of a perfect gas, the value of ∆P P is equal to (a.) −√γ ∆V V (b.) − ∆V V (c.) −γ ∆V V (d.) −γ 2 ∆V V (7.)In the following p − V diagram figure two adiabates cut two isothermals at T1 and T2. The value of Vb/Vc is (a.) = Va/Vd (b.) < Va/Vd (c.) > Va/Vd (d.) Cannot say (8.)A gas expands 0.25m3 at constant pressure 103N/m2 , the work done is (a.) 2.5 ergs (b.) 250 J (c.) 250 W (d.) 250 N (9.)Ten moles of an ideal gas at constant temperature 500 K is compressed from 50 L to 5 L. Work done in the process is (Given, R = 8.31 J − mol −1 − K −1 ) (a.) −1.2 × 104 J (b.) −2.4 × 104 J (c.) −4.8 × 104 J (d.) −9.6 × 104 J (10.)If an ideal gas is compressed isothermally then (a.) No work is done against gas (b.) Heat is released by the gas (c.) The internal energy of gas will increase (d.) Pressure does not change (11.)The work done, W during an isothermal process in which 1 mole of the gas expands from an initial volume V1 to a final volume V2 is given by (R=gas constant, T=temperature) (a.) R(V2 − V1 ) loge ( T1 T2 ) (b.) R(T2 − T1 ) loge ( V2 V1 ) (c.) RT loge( V2 V1 ) (d.) 2RT loge ( V1 V2 ) (12.)Two isothermally are shown in figure at temperature T1 and T2. Which of the following relations is correct? A D C B P V
(a.) T1 > T2 (b.) T1 < T2 (c.) T1 = T2 (d.) T1 = 1 2 T2 (13.)In Carnot engine efficiency is 40% at hot reservoir temperature T. For efficiency 50% what will be temperature of hot reservoir? (a.) T 5 (b.) 2T 5 (c.) 6T (d.) 6T 5 (14.)In changing the state of thermodynamics from A to B state, the heat required is Q and the work done by the system is W. The change in its internal energy is (a.) Q + W (b.) Q − W (c.) Q (d.) Q−W 2 (15.)1 cm3 of water at its boiling point absorbs 540 cal of heat to become steam with a volume = 1.013 × 105Nm−2 and the mechanical equivalent of heat = 4.19 Jcal −1 , the energy spend in this process in overcoming intermolecular forces is (a.) 540 cal (b.) 40 cal (c.) 500 cal (d.) Zero (16.)The adiabatic elasticity of hydrogen gas (γ = 1.4) at NTP is (a.) 1 × 105N/m2 (b.) 1 × 10−8N/m2 (c.) 1.4 N/m2 (d.) 1.4 × 105 N/m2 (17.)Which one of the following statements is true in respect of usual quantities represented by ∆Q, ∆U and ∆W (a.) ∆U and ∆W are path dependent (b.) ∆Q and ∆U are path dependent (c.) ∆U does not dependent on path (d.) ∆Q does not depend upon path (18.)In a thermodynamic system working substance is ideal gas, its internal energy is in the form of (a.) Kinetic energy only (b.) Kinetic and potential energy (c.) Potential energy (d.) None of these (19.)Helium at 27°C has a volume of 8 litres. It is suddenly compressed to a volume of 1 litre. The temperature of the gas will be [γ = 5/3] (a.) 108°C (b.) 9327°C (c.) 1200°C (d.) 927°C (20.)For an ideal gas, in an isothermal process (a.) Heat content remains constant (b.) Heat content and temperature remain constant (c.) Temperature remains constant (d.) None of the above (21.)An engineer claims to have made an engine delivering 10 kW power with fuel consumption of 1 g/s. The calorific value of the fuel is 2 kcal/g. Is the claim of the engineer (a.) Valid (b.) Invalid (c.) Depends on engine design (d.) Depends of the load (22.)A graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph curve OC represents (a.) Isochoric process (b.) Isothermal process (c.) Isobaric process (d.) Adiabatic process (23.)For nitrogen Cp − Cv = x and for argon, Cp − Cv = y. The relation between x and y is given by (a.) x = y (b.) x = 7y (c.) y = 7x (d.) x = 1 2 y (24.)If ∆Q and ∆W represent the heat supplied to the system and the work done on the system respectively, then the first law of thermodynamics can be written as Where ∆U is the internal energy (a.) ∆Q = ∆U + ∆W (b.) ∆Q = ∆U − ∆W (c.) ∆Q = ∆W − ∆U (d.) ∆Q = −∆W − ∆U (25.)In an isothermal change, an ideal gas obeys (a.) Boyle’s law (b.) Charle’s law
(c.) Gaylussac law (d.) None of the above (26.)During an adiabatic process, the pressure p of a fixed mass of an ideal gas changes by ∆p and its volume V changes ∆V. If γ = Cp/Cv, then ∆V/V is given by (a.) − ∆p p (b.) −γ ∆p p (c.) − ∆p γp (d.) − ∆p γ 2p (27.)In an adiabatic process, the state of a gas is changed from p1, V1,T1to p2,V2, T2. Which of the following relation is correct? (a.) T1V1 γ−1 = T2V2 γ−1 (b.) p1V1 γ−1 = p2V2 γ−1 (c.) T1p1 γ = T2V2 γ (d.) T1V1 γ = T2V2 γ (28.)The specific heat of a gas in an isothermal process is (a.) Infinite (b.) Zero (c.) Negative (d.) Remains constant (29.)An ideal refrigerator has a freezer at a temperature of −13°C. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be (a.) 325°C (b.) 325°K (c.) 39°C (d.) 320°C (30.)If for hydrogen Cp − Cv = m and for the nitrogen Cp − Cv = n, where Cp, Cv refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between m and n is (a.) m = 14 n (b.) n = 7 n (c.) m = 7 n (d.) n = 14 n (31.)What is the nature of change in internal energy in the following three thermodynamical processes shown in figure? (a.) ∆U is positive in all the three cases (b.) ∆U is negative in all the three cases (c.) ∆U is positive for (i), negative for (ii), zero for (iii) (d.) ∆U = 0, in all the cases (32.)The volume of air increases by 5%, in its adiabatic expansion. The percentage decrease in its pressure will be (a.) 5% (b.) 6% (c.) 7% (d.) 8% (33.)If a Carnot’s engine functions at source temperature 127°C and at sink temperature 87°C, what is its efficiency (a.) 10% (b.) 25% (c.) 40% (d.) 50% (34.)A gas (γ = 5 3 ), expands isobarically. The percentage of heat supplied that increases thermal energy and that is involved in doing work for expansion is (a.) l40: 60 (b. ) 60: 40 (c.) 50: 50 (d. ) 25: 30 (35.)For which of the following processes is the entropy change zero (a.) Isobaric (b.) Isothermal (c.) Adiabatic (d.) None of the above (36.)200 cal of heat is given to a heat engine so that it rejects 150 cal of heat, if source temperature is 400 K, then the sink temperature is (a.) 300 K (b.) 200 K (c.) 100 K (d.) 50 K (37.)Find the change in the entropy in the following process 100 g of ice at 0°C melts when dropped in a
bucket of water at 50°C (Assume temperature of water does not change) (a.) −4.5 cal/K (b.) +4.5 cal/K (c.) +5.4 cal/K (d.) −5.4 cal/K (38.)The sink temperature of a heat engine 77°C. The efficiency is 30%. The source temperature is (a.) 500°C (b.) 227°C (c.) 317°C (d.) 427°C (39.)Figure shows a thermodynamical process on one moles a gas. How does the work done in the process change with time? (a.) Decrease continuously (b.) Increases continuously (c.) Remains constant (d.) First increase and then decreases (40.)When 1 kg of ice at 0°C melts to water at 0°C, the resulting change in its entropy, taking latent heat of ice to be 80 cal/°C is (a.) 293 cal/K (b.) 273 cal/K (c.) 8 × 104 cal/K (d.) 80 cal/K (41.)A container having 1 mole of a gas at a temperature 27°C has a movable piston which maintains at constant pressure in container of 1 atm. The gas is compressed until temperature becomes 127°C. The work done is (Cpfor gas is 7.03cal/mol − K) (a.) 703 J (b.) 814 J (c.) 121 J (d.) 2035 J (42.)The temperature of a hypothetical gas increases to √2 times when compressed adiabatically to half the volume. Its equation can be written as (a.) PV 3/2 = constant (b.) PV 5/2 = constant (c.) PV 7/3 = constant (d.) PV 4/3 = constant (43.)Three samples of the same gas A, B and C(γ = 3/2) have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for A isobaric for B and isothermal for C. If the final pressure are equal for all three samples, the ratio of their initial pressures are (a.) 2√2 ∶ 2 ∶ 1 (b.) 2√2 ∶ 1 ∶ 2 (c.) √2 ∶ 1 ∶ 2 (d.) 2 ∶ 1 ∶ √2 (44.)In the cyclic process shown in the figure, the work done by the gas in one cycle is (a.) 28 P1V1 (b.) 14 P1V1 (c.) 18 P1V1 (d.) 9 P1V1 (45.)The change in internal energy, when a gas is cooled from 927°C to 27°C (a.) 300% (b.) 400% (c.) 200% (d.) 100% (46.)dU+dW=0 is valid for (a.) Adiabatic process (b.) Isothermal process (c.) Isobaric process (d.) Isochoric process (47.)An ideal heat engine works between temperatures T1 = 500K and T2 = 375K. If the engine absorbs 600 J of heat from the source, then the amount of heat released to the sink is (a.) 450 J (b.) 600 J (c.) 45 J (d.) 500 J (48.)If heat given to a system is 6 kcal and work done is 6 kJ. Then change in internal energy is (a.) 19.1 kJ (b.) 12.5 kJ (c.) 25 kJ (d.) Zero (49.)The pressure and density of a given mass of a diatomic gas (γ = 7 5 ) change adiabatically from (p, d) to (p’, d’). If d′ d = 32, then P′ p is (γ = ratio of specific heats) (a.) 1/128 (b.) 1/64 (c.) 64 (d.) 128 V1 4V1 P1 7P1 P V