Thermodynamics PYQs Set 8 (PDF)

Set 8 of 17 · Questions 211-240 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 8 (Q211-240)
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211. $310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 25^{\circ} C to 35^{\circ} C . The amount of heat required to raise the temperature of the gas through the same range at constant volume is$ (1) $384 J$ (2) $144 J$ (3) $276 J$ (4) $452 J$ 212. $The emissivity of a perfect black body is increased to 16 times by increasing its temperature. If the initial temperature is T, then final temperature of that black body is$ (1) $4 T$ (2) $8 T$ (3) $2 T$ (4) $16 T$ 213. $During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of \frac{C _{p}}{C _{v}} for the gas is$ (1) $\frac{5}{3}$ (2) $\frac{3}{2}$ (3) $\frac{4}{3}$ (4) $2$ 214. $A Carnot engine takes 300 calories of heat from a source at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is$ (1) $125 K$ (2) $250 K$ (3) $750 K$ (4) $1000 K$ 215. $A monatomic gas at pressure P_{1} and volume V_{1} is compressed adiabatically to 1/8th of its original volume. What is the final pressure of the gas?$ (1) $64 P_{1}$ (2) $P_{1}$ (3) $16 P_{1}$ (4) $32 P_{1}$ 216. $A sphere of surface area 4 m^{2} at temperature 400 K and having emissivity 0.5 is located in an environment of temperature 200 K . The net rate of energy exchange of the sphere is (Stefan Boltzmann constant σ = 5.67 \times 10^{- 8} Wm^{- 2} K^{4})$ (1) $3260.8 W$ (2) $1632.4 W$ (3) $2721.6 W$ (4) $4216.4 W$ 217. $Relation between pressure (P) and energy (E) of a gas is$ (1) $P = \frac{2}{3} E$ (2) $P = \frac{1}{3} E$ (3) $P = E$ (4) $P = 3 E$ 218. $In a Carnot's engine, as the gas gives heat energy to the sink, then the temperature of the sink$ (1) $increases$ (2) $decreases$ (3) $remains constant$ (4) $becomes zero$ 219. $If a carnot engine is working between steam point and ice point, then its efficiency will be$ (1) $24.9 %$ (2) $25.7%$ (3) $26.8%$ (4) $28.8%$ 220. $The focal length of a spherical mirror made of steel is 150 cm . If the temperature of the mirror increases by 200 K, its focal length become (coefficient of linear expansion of steel α = 12 \times 10^{- 6} ° C^{- 1} .)$ (1) $186.3 cm$ (2) $153.6 cm$ (3) $150.036 cm$ (4) $150.36 cm$ 221. $Find the ratio of the length of a steel rod and a copper rod if the steel rod is 4 cm longer than the copper rod at any temperature. [The coefficient of linear expansion for steel and copper are 1.1 \times 10^{- 5} /° C and 1.7 \times 10^{- 5} /° C respectively]$ (1) $\frac{17}{11}$ (2) $\frac{11}{17}$ (3) $\frac{11}{4}$ (4) $\frac{17}{4}$ 222. $A Carnot’s engine is made to work between 200°C and 0°C first and then between 0°C and -200°C. The ratio of efficiencies of the engine in the two cases is$ (1) $1.73 : 1$ (2) $1 : 1.73$ (3) $1 : 1$ (4) $1 : 2$ 223. $1 kg of steam at 150^{\circ} C is passed from a steam chamber is to a copper coil immersed in 20 L of water. The steam condenses in the coil and is returned to the steam chamber as water at 90^{\circ} C . Latent heat of steam is 540 cal g^{- 1}, specific heat of the steam is 1 cal g^{- 10} C^{- 1} . Then, the rise in temperature of water is$ (1) $75^{\circ} C$ (2) $60^{\circ} C$ (3) $30^{\circ} C$ (4) $20^{\circ} C$ 224. $A Carnot’s cycle operating between T_{1} = 600 K and T_{2} = 300 K producing 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoirs$ (1) $2.5 kJ$ (2) $3 kJ$ (3) $3.5 kJ$ (4) $4 kJ$ 225. $A Carnot engine working between 300 K and 600K has work output of 800 J per cycle. What is amount of heat energy supplied to the engine from source per cycle$ (1) $1800 J/cycle$ (2) $1000 J/cycle$ (3) $2000 J/cycle$ (4) $1600 J/cycle$ 226. $The heat energy required convert 10 kg of ice at - 10^{\circ} C into water at 0^{\circ} C is (specific heat capacity of ice = 0.5 cal g^{- 1} and latent heat of fusion of ice = 80 cal g^{- 1})$ (1) $357 \times 10^{4} J$ (2) $357 \times 10^{3} J$ (3) $357 \times 10^{2} J$ (4) $357 \times 10^{5} J$ 227. $A vessel that can withstand a pressure of 100 atm is filled with hydrogen at 27^{\circ} C up to a pressure of 20 atm . If the vessel is heated, then the temperature at which it explodes is$ (1) $500 K$ (2) $1000 K$ (3) $1500 K$ (4) $2000 K$ 228. $A gas at N.T.P. is suddenly compressed to one-fourth of its original volume. If γ = 1.5, then the final pressure is$ (1) $4 times$ (2) $1.5 times$ (3) $8 times$ (4) $\frac{1}{4} times$ 229. $Isothermal bulk modulus of a gas at a pressure P is (γ -ratio of specific heat capacities of the gas)$ (1) $γ$ (2) $γP$ (3) $P$ (4) $\frac{γ}{P}$ 230. $In which of the processes, does the internal energy of the system remain constant?$ (1) $Isobaric$ (2) $Isothermal$ (3) $Adiabatic$ (4) $Isochoric$ 231. $A monatomic gas of volume ' V' and pressure ' P' expands isothermally to a volume ' 27 V' and then compressed adiabatically to a volume ' V'. The final pressure of the gas is$ (1) $3 P$ (2) $2 P$ (3) $9 P$ (4) $4 P$ 232. $A cylinder of fixed capacity of 44.8 liters contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be: (Given gas constant R = 8.3 J K^{- 1} m o l^{- 1})$ (1) $249J$ (2) $415J$ (3) $498J$ (4) $830J$ 233. $Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:$ (1) $525J$ (2) $441J$ (3) $572 J$ (4) $735 J$ 234. $The thermodynamic process, in which internal energy of the system remains constant is$ (1) $Isochoric$ (2) $Adiabatic$ (3) $Isothermal$ (4) $Isobaric$ 235. $In an adiabatic expansion of an ideal gas the product of pressure and volume$ (1) $remains constant$ (2) $at first increases and then decreases$ (3) $decreases$ (4) $increases.$ 236. $A slab of stone of area 3600 cm^{2} and thickness 10 cm is exposed on the lower surface to steam at 100^{\circ} C . A block of ice at 0^{\circ} C rests on upper surface of the slab. In one hour 4.8 kg of ice is melted. The tiermal conductivity of the stone in Js^{- 1} m^{- 1} k^{- 1} is (Latent heat of ice = 3.36 \times 10^{5} J / kg)$ (1) $12.0$ (2) $10.5$ (3) $1.02$ (4) $1.24$ 237. $On a new temperature scale, the melting point of ice is 20^{\circ} X and the boiling point of water is 110^{\circ} X . A temperature of 40^{\circ} C would be indicated on this new temperature scale as$ (1) $60^{\circ} X$ (2) $56^{\circ} X$ (3) $70^{\circ} X$ (4) $54^{\circ} X$ 238. $A gas is compressed from a volume of 2 m^{3} to a volume of 1 m^{3} at a constant pressure of 100 Nm^{- 2} . Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas$ (1) $increases by 250 J$ (2) $decreases by 250 J$ (3) $decreases by 50 J$ (4) $increases by 50 J$ 239. $The efficiency of a heat engine is ' η' and the coefficient of performance of a refrigerator is ' β'. Then$ (1) $η = \frac{1}{β}$ (2) $η = \frac{1}{β + 1}$ (3) $η β = \frac{1}{2}$ (4) $η = \frac{1}{β - 1}$ 240. $If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cycle process, then$ (1) $E = 0$ (2) $Q = 0$ (3) $W = 0$ (4) $Q = W = 0$