Thermal Properties & Calorimetry PYQs Set 4 (PDF)

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Set 4 of 5 · Questions 91-120 of 145

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermal Properties & Calorimetry · Set 4 (Q91-120)
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91. $A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27^{\circ} C to 87^{\circ} C . The rate of consumption of the gas is____g / s . (Take heat of combustion of gas = 5.0 \times 10^{4} J / g) specific heat capacity of water = 4200 J / kg \cdot^{\circ} C$ (1) $0.42$ (2) $2.1$ (3) $0.21$ (4) $4.2$ 92. $When M_{1} gram of ice at - 10° C (Specific heat 0.5 cal g^{- 1} ° C^{- 1}) is added to M_{2} gram of water at 50° C, finally no ice is left and the water is at 0° C. The value of latent heat of ice, in cal g^{- 1} is:$ (1) $\frac{50 M _{2}}{M _{1}} - 5$ (2) $\frac{5 M _{1}}{M _{2}} - 50$ (3) $\frac{50 M _{2}}{M _{1}}$ (4) $\frac{5 M _{2}}{M _{1}} - 5$ 93. $The two ends of a metal rod are maintained at temperatures 100^{\circ} C and 110^{\circ} C . The rate of heat flow in the rod is found to be 4.0 J / s . If the ends are maintained at temperatures 200^{\circ} C and 210^{\circ} C, the rate of heat flow will be$ (1) $44.0 J / s$ (2) $16.8 J / s$ (3) $8.0 J / s$ (4) $4.0 J / s$ 94. $A thermally insulted vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0° C itself. The mass of evaporated water will be closed to:(Latent heat of vaporization of water & Latent heat of Fusion of water )$ (1) $150 g$ (2) $20 g$ (3) $130 g$ (4) $35 g$ 95. $Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20^{\circ} C to 90^{\circ} C . Work done by gas is close to: (Gas constant R = 8.31 J / mol - K)$ (1) $581 J$ (2) $291 J$ (3) $146 J$ (4) $73 J$ 96. $A Carnot engine has an efficiency of 1/6 When the temperature of the sink is reduced by 62^{\circ} C, its efficiency is doubled. The temperatures of the source and the sink are, respectively.$ (1) $62^{\circ} C, 124^{\circ} C$ (2) $99^{\circ} C, 37^{\circ} C$ (3) $124^{\circ} C, 62^{\circ} C$ (4) $37^{\circ} C, 99^{\circ} C$ 97. $100 g of ice at 0^{\circ} C is mixed with 100 g of water at 100^{\circ} C . The final temperature of the mixture is [Take L_{f} = 3.36 \times 10^{5} J kg^{- 1} and S_{w} = 4.2 \times 10^{3} J kg^{- 1} K^{- 1}]$ (1) $40^{\circ} C$ (2) $10^{\circ} C$ (3) $50^{\circ} C$ (4) $1^{\circ} C$ 98. $The specific heat capacity of a metal at low temperature (T) is given as C_{p} (k j K^{-1} k g^{-1}) = 32 (\frac{T}{400})^{3} A 100 gram vessel of this metal is to be cooled from 20K to 4K by a special refrigerator operating at room temperature (27ºC). The amount of work required to cool the vessel is:$ (1) $greater than 0.148 kJ$ (2) $between 0.148 kJ and 0.028 kJ$ (3) $less than 0.028 kJ$ (4) $equal to 0.002 kJ$ 99. $A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75º C. T is given by: (Given: room temperature = 30ºC, specific heat of copper = 0.1 cal/gmºC)$ (1) $825º C$ (2) $800ºC$ (3) $885ºC$ (4) $1250ºC$ 100. $The side of a copper cube is 1 m at 0^{\circ} C . What will be the change in its volume, when it is heated to 100^{\circ} C ? (α_{copper} = 18 \times \frac{10 ^{- 6}}{^{\circ} C})$ (1) $45 \times 10^{- 4} m^{3}$ (2) $54 \times 10^{- 4} m^{3}$ (3) $34 \times 10^{- 4} m^{3}$ (4) $64 \times 10^{- 4} m^{3}$ 101. $Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C . The thermal conductivity of B is thrice that of C and half of that of A . The effective thermal conductivity of the system will be (K_{A} is the thermal conductivity of rod A)$ (1) $\frac{1}{3} K_{A}$ (2) $3 K_{A}$ (3) $2 K_{A}$ (4) $\frac{2}{3} K_{A}$ 102. $Following figure shows two processes A and B for a gas. If Δ Q_{A} and Δ Q_{B} are the amount of heat absorbed by the system in two cases, and Δ U_{A} and Δ U_{B} are changes in internal energies, respectively, then:$ (1) $Δ Q_{A} < Δ Q_{B}, Δ U_{A} < Δ U_{B}$ (2) $Δ Q_{A} > Δ Q_{B}, Δ U_{A} > Δ U_{B}$ (3) $Δ Q_{A} > Δ Q_{B}, Δ U_{A} = Δ U_{B}$ (4) $Δ Q_{A} = Δ Q_{B}; Δ U_{A} = Δ U_{B}$ 103. $Two identical rods AC and CB made of two different metals having thermal conductivities in the ratio 2 : 3 are kept in contact with each other at the end C as shown in the figure. A is at 100^{\circ} C and B is at 25^{\circ} C . Then the junction C is at$ (1) $55^{\circ} C$ (2) $60^{\circ} C$ (3) $75^{\circ} C$ (4) $50^{\circ} C .$ 104. $A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is - 180 J The gas absorbs 250 J of heat along the path ab and 60 J along the path bc . The work down by the gas along the path abc is:$ (1) $120 J$ (2) $130 J$ (3) $100 J$ (4) $140 J$ 105. $A metal rod of Young’s modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by tºC, the linear stress developed in its is:$ (1) $\frac{Y}{α t}$ (2) $Yαt$ (3) $\frac{1}{( Y α t )}$ (4) $\frac{α t}{Y}$ 106. $Two thin metallic spherical shells of radii r_{1} and r_{2} (r_{1} < r_{2}) are placed with their centers coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature θ_{1} and the outer shell at temperature θ_{2} (θ_{1} < θ_{2}) . The rate at which heat flows radially through the material is:-$ (1) $\frac{4 πK r _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}$ (2) $\frac{π r _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}$ (3) $\frac{K ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}$ (4) $\frac{K ( θ _{2} - θ _{1} ) ( r _{2} - r _{1} )}{4 π r _{1} f _{2}}$ 107. $The coefficient of the thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?$ (1) $25^{\circ} C$ (2) $33^{\circ} C$ (3) $75^{\circ} C$ (4) $67^{\circ} C$ 108. $Two metallic wires of identical dimensions are connected is series. If σ_{1} and σ_{2} are the conductivities of these wires respectively, the effective conductivity of the combination is:$ (1) $\frac{σ _{1} σ _{2}}{σ _{1} + σ _{2}}$ (2) $\frac{2 σ _{1} σ _{2}}{σ _{1} + σ _{2}}$ (3) $\frac{σ _{1} + σ _{2}}{2 σ _{1} σ _{2}}$ (4) $\frac{σ _{1} + σ _{2}}{σ _{1} σ _{2}}$ 109. $A thermometer graduated according to a linear scale reads a value x_{0} when in contact with boiling water, and x_{0} /3 when in contact with ice. What is the temperature of an object in ° C if this thermometer in the contact with the object reads x_{0} /2 ?$ (1) $25$ (2) $60$ (3) $40$ (4) $35$ 110. $The temperature of equal masses of three different liquids x,y and z are 1 0^{0} C, 2 0^{0} C and 3 0^{0} C respectively. The temperature of mixture when x is mixed with y is 1 6^{0} C and that when y is mixed with z is 2 6^{0} C. The temperature of mixture when x and z are mixed will be:$ (1) $28. 3 2^{0} C$ (2) $25. 6 2^{0} C$ (3) $23. 8 4^{0} C$ (4) $20. 2 8^{0} C$ 111. $The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:$ (1) $adbc$ (2) $dacb$ (3) $adcb$ (4) $dabc$ 112. $For the given cyclic process CAB as shown for gas, the work done is:$ (1) $30 J$ (2) $10 J$ (3) $1 J$ (4) $5 J$ 113. $A solid metallic cube having total surface area 24 m^{2} is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube (Given α = 5.0 x 1 0^{- 4} ° C^{- 1})$ (1) $2. 4 x 1 0^{6} c m^{3}$ (2) $1.2 x 1 0^{5} c m^{3}$ (3) $6. 0 x 1 0^{4} c m^{3}$ (4) $4. 8 x 1 0^{5} c m^{3}$ 114. $Which one of the following is v_{m} - T graph for perfectly black body? v_{m} is the frequency of radiation with maximum intensity. T is the absolute temperature.$ (1) $A$ (2) $B$ (3) $C$ (4) $D$ 115. $Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m i is a x 1 0^{- 2} W/ m^{2} . The value of 'a' will be$ 116. $A piece of ice (heat capacity = 2100 J k g^{-1} º C^{-1} and latent heat = 3.36 \times 1 0^{5} J k g^{-1}) of mass m grams is at -5 ºC at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally, when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is:$ 117. $A hole is drilled in a metal sheet. At 27°C, the diameter of hole is 5 cm. When the sheet is heated to 177°C, the change in the diameter of hole is d x 1 0^{- 3} cm. The value of d will be _______ if coefficient of linear expansion of the metal is 1.6 x 1 0^{- 5} /°C.$ 118. $At room temperature (27^{\circ} C), the resistance of a heating element is 50Ω . The temperature coefficient of the material is 2.4 \times 10^{- 4^{\circ}} C^{- 1} . The temperature of the element, when its resistance is 62Ω, is ____^{\circ} C .$ 119. $A road CD of thermal resistance 10. 0 K W^{- 1} is joined at the middle of an identical rod AB as shown in figure, The end A, B and D are maintained at 20 0^{0} C, 10 0^{0} C and 12 5^{0} C respectively. The heat current in CD is P watt. The value of P is$ 120. $Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are: \frac{L _{A}}{L _{B}} = \frac{1}{2}, \frac{r _{A}}{r _{B}} = 2 and \frac{K _{A}}{K _{B}} = \frac{1}{2} . The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is K , when equilibrium is established.$