Thermal Properties & Calorimetry PYQs Set 5 (PDF)

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Set 5 of 5 · Questions 121-145 of 145

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermal Properties & Calorimetry · Set 5 (Q121-145)
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121. $Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_{1} and K_{2} . The thermal conductivity of the composite rod will be [NEET 2017]$ (1) $\frac{K _{1} + K _{2}}{2}$ (2) $\frac{3 ( K _{1} + K _{2} )}{2}$ (3) $K_{1} + K_{2}$ (4) $2 (K_{1} + K_{2})$ 122. $Three Carnot engines operate in series between a heat source at a temperature T_{1} and a heat sink at temperature T_{4} (see figure). There are two other reservoirs at temperature T_{2} and T_{3}, as shown, with T_{1} > T_{2} > T_{3} > T (4) The three engines are equally efficient if:$ (1) $T_{2} = (T_{1} T_{4})^{1/2}; T_{3} = (T_{1}^{2} T_{4})^{1/3}$ (2) $T_{2} = (T_{1}^{2} T_{4})^{1/3}; T_{3} = (T_{1} T_{4}^{2})^{1/3}$ (3) $T_{2} = (T_{1} T_{4}^{2})^{1/3}; T_{3} = (T_{1}^{2} T_{4})^{1/3}$ (4) $T_{2} = (T_{1}^{3} T_{4})^{1/4}; T_{3} = (T_{1} T_{4}^{3})^{1/4}$ 123. $If K_{1} and K_{2} are the thermal conductivities L_{1} and L_{2} are the lengths and ai and A_{2} are the cross sectional areas of steel and copper rods respectively such that \frac{K _{2}}{K _{1}} = 9, \frac{A _{1}}{A _{2}} = 2, \frac{L _{1}}{L _{2}} = 2 . Then, for the arrangement as shown in the figure. The value of temperature T of the steel - copper junction in the steady state will be:$ (1) $18°C$ (2) $14°C$ (3) $45°C$ (4) $150°C$ 124. $Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100^{\circ} C and 40^{\circ} C respectively. Given the thermal conductivity of rodx is three times of that of rody, the temperature at junction points B and E are (close to):$ (1) $80^{\circ} C and 70^{\circ} C respectively$ (2) $80^{\circ} C and 60^{\circ} C respectively$ (3) $60^{\circ} C and 45^{\circ} C respectively$ (4) $89^{\circ} C and 73^{\circ} C respectively$ 125. $An ice cube of dimensions 60 cm x 50 cm x 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately: (Latent heat of fusion of ice is 3.4 x 1 0^{5} J k g^{- 1} and thermal conducting of insulation wall is 0.05 W m^{- 1}^{0} C^{- 1})$ (1) $61 x 1 0^{- 1} kg s^{- 1}$ (2) $61 x 1 0^{- 5} kg s^{- 1}$ (3) $208 kg s^{- 1}$ (4) $30x 1 0^{- 5} kg s^{- 1}$ 126. $Two slabs are of the thicknesses d_{1} and d_{2} . Their thermal conductivities are K_{1} and K_{2} respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures θ_{1} and θ_{2} . Assume θ_{1} > θ_{2} . The temperature θ of their common junction is$ (1) $\frac{K _{1} θ _{1} + K _{2} θ _{2}}{θ _{1} + θ _{2}}$ (2) $\frac{K _{1} θ _{1} d _{1} + K _{2} θ _{2} d _{2}}{K _{1} d _{2} + K _{2} d _{1}}$ (3) $\frac{K _{1} θ _{1} d _{2} + K _{2} θ _{2} d _{1}}{K _{1} d _{2} + K _{2} d _{1}}$ (4) $\frac{K _{1} θ _{1} + K _{2} θ _{2}}{K _{1} + K _{2}}$ 127. $Two metallic blocks M_{1} and M_{2} of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M_{2} is K then the thermal conductivity of mi will be: [Assume steady state heat conduction]$ (1) $10 K$ (2) $8 K$ (3) $12.5 K$ (4) $2 K$ 128. $A gas can be taken from A to B via two different processes ACB and ADB . When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J . The heat Flow into the system in path ADB is:$ (1) $40 J$ (2) $80 J$ (3) $100 J$ (4) $20 J$ 129. $A, B and C are the three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are K, 2 K and K /2 . The free end of A is at 100^{\circ} C and the free end of C is at 0^{\circ} C . During steady state, the temperature of the junction of A and B is nearly ...^{\circ} C .$ (1) $71$ (2) $29$ (3) $63$ (4) $37$ 130. $Consider a rectangular sheet of solid material of length l = 9 cm and width d = 4 cm . The coefficient of linear expansion is α = 3.1 \times 10^{- 5} K^{- 1} at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity C_{v} = 900 J kg^{- 1} K^{- 1} . If the amount of heat supplied to the material is 8.1 \times 10^{2} J then change in area of the rectangular sheet is:-$ (1) $2.0 \times 10^{- 6} m^{2}$ (2) $3.0 \times 10^{- 7} m^{2}$ (3) $6.0 \times 10^{- 7} m^{2}$ (4) $4.0 \times 10^{- 7} m^{2}$ 131. $10 kg of ice at - 10^{\circ} C is added to 100 kg of water to lower its temperature from 25^{\circ} C . Consider no heat exchange to surroundings. The decrement to the temperature of water is____^{\circ} C . (specific heat of ice = 2100 J / Kg .^{\circ} C, specific heat of water = 4200 J / Kg .^{\circ} C, latent heat of fusion of ice = 3.36 \times 10^{5} J / Kg)$ (1) $6.67$ (2) $11.6$ (3) $15$ (4) $10$ 132. $A deep rectangular pond of surface area A, containing water (density = ρ, specific heat capacity = s), is located in a region where the outside air temperature is a steady value at the - 26^{\circ} C . The thickness of the frozen ice layer in this pond, at a certain instant is x . Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant would be given by [NEET 2019]$ (1) $26 K / ρr (L - 4 s)$ (2) $26 K / (ρ x^{2} - L)$ (3) $26 K / (ρxL)$ (4) $26 K / ρr (L + 4 s)$ 133. $The unit of Stefan's constant is$ (1) $W m^{- 2} K^{- 1}$ (2) $WmK^{- 4}$ (3) $W m^{- 2} K^{- 4}$ (4) $N m^{- 2} K^{4} .$ 134. $A massless spring (K=800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and spring receive negligible heat & specific heat of mass = 400 J / kg K, specific heat of water = 4184 J / kg K)$ (1) $10^{- 1} K$ (2) $10^{- 5} K$ (3) $10-2K$ (4) $10^{- 3} K$ 135. $A water cooler of storage capacity 120 liters can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 liters of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is: (Specific heat of water is 4.2 kJ k g^{-1} K^{-1} and the density of water is 1000 kg m^{-3})$ (1) $1600$ (2) $2067$ (3) $2533$ (4) $3933$ 136. $An amount of ice of mass 10^{- 3} kg and temperature - 10^{\circ} C is transformed to vapour of temperature 110^{\circ} C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = 2100 Jkg^{- 1} K^{- 1}, specific heat of water = 4180 Jkg^{- 1} K^{- 1}, specific heat of steam = 1920 Jkg^{- 1} K^{- 1}, Latent heat of ice = 3.35 \times 10^{5} Jkg^{- 1} and Latent heat of steam = 2.25 \times 10^{6} Jkg^{- 1})$ (1) $3043 J$ (2) $3024 J$ (3) $3003 J$ (4) $3022 J$ 137. $A solid cylinder of radius R made of a material of thermal conductivity K_{1} is surrounded by a cylindrical shell of inner radius R and outer radius 2 R made of a material of thermal conductivity K_{2} . The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is$ (1) $K_{1} + K_{2}$ (2) $K1K2 K_{1} + K_{2}$ (3) $3 K_{1} + K_{2} 4$ (4) $\frac{K _{1} + 3 K _{2}}{4}$ 138. $In anomalous expansion of water, at what temperature, the density of water is maximum?$ (1) $> 4^{\circ} C$ (2) $4^{\circ} C$ (3) $10^{\circ} C$ (4) $< 4^{\circ} C$ 139. $A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is l_{1} and that below the piston is l_{2} such that l_{1} > l_{2} Each part of the cylinder contains n moles of an ideal gas at equal temperature T . If the piston is stationary, its mass, T, will be given by: (R is universal gasconstant and g is theacceleration due to gravity)$ (1) $\frac{RT}{ng} (\frac{l _{1} - 3 l _{2}}{l _{1} I _{2}})$ (2) $\frac{RT}{g} (\frac{2 l _{1} + l _{2}}{l _{1} I _{2}})$ (3) $\frac{nRT}{g} (\frac{1}{l _{2}} + \frac{1}{l _{1}})$ (4) $\frac{nRT}{g} (\frac{l _{1} - l _{2}}{l _{1} l _{2}})$ 140. $Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?$ (1) (2) (3) (4) 141. $A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ∆ T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:$ (1) $2πSYαΔT$ (2) $SYαΔT$ (3) $πSYαΔT$ (4) $2SYαΔT$ 142. $In an experiment to verify Newton's law of cooling, a graph is plotted between, the temperature difference (^{∆ T}) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80°C. The value of t_{2} as mentioned in the graph will be_______.$ 143. $A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be __________ cm (α_{iron} = 1.2 \times 1 0^{- 5} K^{- 1} and α_{brass} = 1.8 \times 1 0^{- 5} K^{- 1})$ 144. $Three conductors of same length having thermal conductivity k_{1}, k_{2} and k_{3} are connected as shown in figure. Area of cross sections of 1^{st} and 2^{nd} conductor are same and for 3^{rd} conductor it is double of the 1^{st} conductor. The temperatures are given in the figure. In steady state condition, the value of θ Is^{\circ} C .= (Given: k_{1} = 60 Js^{- 1} m^{- 1} K^{- 1}, k_{2} = 120 Js^{- 1} m^{- 1} K^{- 1}, k_{3} = 135 Js^{- 1} m^{- 1} K^{- 1})$ 145. $A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm / cm^{3} .) The unknown mass is ________ kg.$