Thermodynamics PYQs Set 10 (PDF)

Set 10 of 17 · Questions 271-300 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 10 (Q271-300)
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271. $Boiling water is changing into steam. The specific heat of boiling water is$ (1) $zero$ (2) $one$ (3) $infinity$ (4) $less than one$ 272. $A gas at N.T.P. is suddenly compressed to (\frac{1}{4})^{th} of its original volume. The final pressure in (Given γ = ratio of specific heats = \frac{3}{2}) atmosphere is (P = original pressure)$ (1) $4 P$ (2) $\frac{3}{2} P$ (3) $8 P$ (4) $1 4 P$ 273. $A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2^{\circ} C . The work done by the gas is: Given, R = 8.3 J K^{- 1} mol^{- 1} .$ (1) $24.9 J$ (2) $72.9 J$ (3) $48 J$ (4) $23.1J$ 274. $The equation for real gas is given by (P + \frac{a}{V ^{2}}) (V - b) = RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab^{- 2} is equivalent to that of:$ (1) $Compressibility$ (2) $Planck's constant$ (3) $Energy density$ (4) $Strain$ 275. $At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given: Mass of oxygen molecule (m) = 2.76 \times 1 0^{- 26} kg, Boltzmann’s constant k_{B} = 1.38 \times 1 0^{- 23} J K^{- 1})$ (1) $2.518 \times 1 0^{4} K$ (2) $8.360 \times 1 0^{4} K$ (3) $5.016 \times 1 0^{4} K$ (4) $1.254 \times 1 0^{4} K$ 276. $The efficiency of a Carnot engine which operates between the two temperatures T_{1} = 500 K and T_{2} = 300 K is$ (1) $25 %$ (2) $40 %$ (3) $50 %$ (4) $75 %$ 277. $A refrigerator is to maintain eatables kept inside at 7°C. The coefficient of performance of refrigerator if room temperature is 38°C is$ (1) $15.5$ (2) $16.3$ (3) $20.1$ (4) $9.03$ 278. $A thermos flask contains 250 g of coffee at 90^{\circ} C . To this 20 g oí milk at 5^{\circ} C is added. After equilibrium is established, the temperature of the liquid is (Assume no heat loss to the thermos bottle. Take specific heat of coffee and milk as 1.00 cal / g^{\circ} C)$ (1) $3.23^{\circ} C$ (2) $3.15^{\circ} C$ (3) $83.7^{\circ} C$ (4) $37.8^{\circ} C$ 279. $Which of the following is not a thermodynamic co-ordinate?$ (1) $Gas constant (R)$ (2) $Pressure (P)$ (3) $Volume (V)$ (4) $Temperature (T)$ 280. $The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is$ (1) $26.8%$ (2) $20%$ (3) $6.25%$ (4) $12.5%$ 281. $A polyatomic gas follows a law T^{2} Vα = constant. Find α for which the heat exchange of gas in the process becomes zero.$ (1) $α = \frac{3}{2}$ (2) $α = \frac{2}{3}$ (3) $α = \frac{4}{3}$ (4) $α = \frac{3}{4}$ 282. $The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is - 2 0^{o} C, the temperature ofthe surroundings to which it rejects heat is$ (1) $1 1^{o} C$ (2) $2 1^{o} C$ (3) $3 1^{o} C$ (4) $4 1^{o} C$ 283. $If the ratio of densities of two substances is 5:6 and the ratio of their specific heat capacities is 3 : 5, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is$ (1) $1 : 1$ (2) $1 : 4$ (3) $1 : 2$ (4) $1 : 3$ 284. $Temperature of a cold reservoir of a Carnot engine is 127^{\circ} C . If the efficiency of the Carnot engine is 20 %, then the temperature of the hot reservoir is$ (1) $500^{\circ} C$ (2) $227^{\circ} C$ (3) $273^{\circ} C$ (4) $400^{\circ} C$ 285. $A gas is compressed at a constant pressure of 50 N / m^{2} from a volume of 10 m^{3} to a volume of 4 m^{3} . Energy of 100 J is then added to the gas by heating. Its internal energy is$ (1) $increased by 400 J$ (2) $increased by 200 I$ (3) $increased by 100 J$ (4) $decreased by 200 I$ 286. $For which combination of working temperatures of source and sink, the efficiency of Carnot's heat engine is maximum?$ (1) $600 K, 400 K$ (2) $500 K, 300 K$ (3) $400 K, 200 K$ (4) $300 K, 100 K$ 287. $To find out degree of freedom, the expression is$ (1) $f = \frac{2}{γ - 1}$ (2) $f = \frac{γ + 1}{2}$ (3) $f = \frac{2}{γ + 1}$ (4) $f = \frac{1}{γ + 1} .$ 288. $A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount ofheat energy supplied to the engine from the source in each cycle is:$ (1) $3200 J$ (2) $1800 J$ (3) $1600 J$ (4) $2400 J$ 289. $Consider the sound wave travelling in ideal gases of He, CH_{4}, and CO_{2} . All the gases have the same ratio \frac{P}{ρ}, where P is the pressure and ρ is the density. The ratio of the speed of sound through the gases V_{He} : V_{CH_{4}} : V_{CO_{2}} is given by$ (1) $\frac{7}{5} : \frac{5}{3} : \frac{4}{3}$ (2) $\frac{5}{3} : \frac{4}{3} : \frac{4}{3}$ (3) $\frac{5}{3} : \frac{4}{3} : \frac{7}{5}$ (4) $\frac{4}{3} : \frac{5}{3} : \frac{7}{5}$ 290. $A gas is compressed adiabatically, which one of the following statement is NOT true?$ (1) $There is no heat supplied to the system$ (2) $There is no change in the internal energy$ (3) $The temperature of the gas increases$ (4) $The change in the internal energy is equal to the work done on the gas$ 291. $For which combination of working temperatures, the efficiency of 'Carnot's engine' is the least?$ (1) $40 K, 20 K$ (2) $60 K, 40 K$ (3) $100 K, 80 K$ (4) $80 K, 60 K$ 292. $A steel rod at 25^{\circ} C is observed to be 1 m long when measured by another metal scale which is correct at 0^{\circ} C . The exact length of steel rod at 0^{\circ} C is (α_{steel} = 12 \times 10^{- 6} /° C and α_{metal} = 20 \times 10^{- 6} /° C)$ (1) $1.00002 m$ (2) $1.0002 m$ (3) $0.998 m$ (4) $0.9998 m$ 293. $The relation between volume (V) and absolute temperature (T) of a gas in an adiabatic process is$ (1) $TV^{γ} = constant$ (2) $VT^{γ} = constant$ (3) $TV^{1 - γ} = constant$ (4) $TV^{γ - 1} = constant$ 294. $An Ideal gas heat engine operated in a carnot's cycle between 227° C and 127° C. It absorbs 6 \times 1 0^{4} J at high temperature. The amount of heat converted into work is$ (1) $4.8 \times 104 J$ (2) $3.5 \times 1 0^{4} J$ (3) $1.6 \times 1 0^{4} J$ (4) $1.2 \times 104 J$ 295. $Steam at 100^{\circ} C is passed into 1 kg of water contained in a calorimeter at 9^{\circ} C till the temperature of water and calorimeter is increased to 90^{\circ} C . The mass of the steam condensed is nearly (water equivalent of calorimeter = 0.1 kg, specific heat of water = 1 calg^{- 1} ° C^{- 1} and latent heat of vaporisation = 540 calg^{- 1})$ (1) $81 g$ (2) $162 g$ (3) $243 g$ (4) $486 g$ 296. $One mole of a gas expands such that its volume ' V' changes with absolute temperature ' T' in accordance with the relation V = K T^{2} where ' K' is a constant. If the temperature of the gas changes by 60^{\circ} C, then work done by the gas is (R is universal gas constant).$ (1) $KRln 60$ (2) $Rln 60$ (3) $40 KR$ (4) $120 R$ 297. $A Carnot working between 300K and 600K has work output of 800 J per cycle. What is amount of heat energy supplied to the engine form source per cycle$ (1) $1800 J/cycle$ (2) $1000 J/cycle$ (3) $2000 J/cycle$ (4) $1600 J/cycle$ 298. $According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-$ (1) $\frac{9}{2} R$ (2) $\frac{5}{2} R$ (3) $\frac{3}{2} R$ (4) $\frac{7}{2} R$ 299. $In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is_______x 1 0^{6} J.$ 300. $300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is 227 °C, then the temperature of sink will be__°C.$