Heat Transfer PYQs Set 6 (PDF)

Set 6 of 7 · Questions 151-180 of 209

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Mere Teacher · Previous Year Questions JEE Main Physics · Heat Transfer · Set 6 (Q151-180)
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151. $There is a rough black spot on a polished metallic plate. It is heated upto 1400 K approximately and then at once taken in a dark room. Which of the following statements is true$ (1) $In comparison with the plate, the spot will shine more$ (2) $In camparison with the plate, the spot will appear more black$ (3) $The spot and the plate will be equally bright$ (4) $The plate and the black spot cannot be seen in the dark room$ 152. $Temperature of a black body increases from 32 7^{o} C to 92 7^{o} C, the initial energy possessed is 2KJ, what is its final energy$ (1) $32 KJ$ (2) $320 KJ$ (3) $1200 KJ$ (4) $None of these$ 153. $Two stars emit maximum radiation at wavelength 3600 A ˚ and 4800 A ˚ respectively. The ratio of their temperatures is$ (1) $1 : 2$ (2) $3 : 4$ (3) $4 : 3$ (4) $2 : 1$ 154. $On observing light from three different stars P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum in the spectrum of Q. If T_{p}, T_{Q} and T_{R} are the respective absolute temperature of P, Q and R, then it can be concluded from the above observations that:$ (1) $T_{P} > T_{R} > T_{Q}$ (2) $T_{P} < T_{R} < T_{Q}$ (3) $T_{P} < T_{Q} < T_{R}$ (4) $TP >TQ >TR$ 155. $A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be$ (1) $T$ (2) $\frac{7}{4} T$ (3) $\frac{3}{2} T$ (4) $\frac{4}{3} T$ 156. $Newton's law of cooling is a special case of$ (1) $Stefan's law$ (2) $Kirchhoff's law$ (3) $Wien's law$ (4) $Planck's law$ 157. $The temperature of the body is increased from -73^{o} C to 327^{o} C, the ratio of energy emitted per second is:$ (1) $1 : 3$ (2) $1 : 81$ (3) $1 : 27$ (4) $1 : 9$ 158. $A body takes 4 minutes to cool from 10 0^{o} C to 7 0^{o} C . To cool from 7 0^{o} C to 4 0^{o} C it will take (room temperature is 1 5^{o} C)$ (1) $7 minutes$ (2) $6 minutes$ (3) $5 minutes$ (4) $4 minutes$ 159. $The radiation energy density per unit wavelength at a temperature T has a maximum at a wavelength λ_{0} . At temperature 2 T, it will have a maximum at a wavelength$ (1) $4λ0$ (2) $2λ0$ (3) $λ0/2$ (4) $λ0/4$ 160. $The plots of intensity versus wavelength for three black bodies at temperatures T_{1}, T_{2} and T_{3} respectively are as shown. Their temperature are such that$ (1) $T_{1} > T_{2} > T_{3}$ (2) $T_{1} > T_{3} > T_{2}$ (3) $T_{2} > T_{3} > T_{1}$ (4) $T_{3} > T_{2} > T_{1}$ 161. $A block body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U_{1} at wavelength 500 nm is U_{2} and that at 1000 nm is U_{3} . Wien’s constant, b = 2.88 \times 1 0^{6} nmK. Which of the following is correct?$ (1) $U_{2} > U_{1}$ (2) $U_{1} = 0$ (3) $U_{3} = 0$ (4) $U_{1} > U_{2}$ 162. $The graph. Shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity (e) and absorptivity (a) of the two bodies$ (1) $e_{x} > e_{y} & a_{x} < a_{y}$ (2) $e_{x} < e_{y} & a_{x} > a_{y}$ (3) $e_{x} > e_{y} & a_{x} > a_{y}$ (4) $e_{x} < e_{y} & a_{x} < a_{y}$ 163. $A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius. 2 R The thermal conductivity of the material of the inner cylinder is K_{1} and that of the outer cylinder is K_{2} . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:$ (1) $\frac{K _{1} + K _{2}}{2}$ (2) $K_{1} + K_{2}$ (3) $\frac{2 K _{1} + 3 K _{2}}{5}$ (4) $\frac{K _{1} + 3 K _{2}}{4}$ 164. $Which of the law can be understood in terms of Stefan's law$ (1) $Wien’s displacement law$ (2) $Kirchoff’s law$ (3) $Newton’s law of cooling$ (4) $Planck’s law$ 165. $Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is$ (1) $(\frac{65}{2})^{\frac{1}{4}} T$ (2) $(\frac{97}{4})^{\frac{1}{4}} T$ (3) $(\frac{97}{2})^{\frac{1}{4}} T$ (4) $(97)^{\frac{1}{4}} T$ 166. $Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_{1} and K_{2} . The thermal conductivity of the composite rod will be$ (1) $\frac{( K _{1} + K _{2} )}{2}$ (2) $\frac{3 ( K _{1} + K _{2} )}{2}$ (3) $K_{1} + K_{2}$ (4) $2(K_{1} + K_{2})$ 167. $One end of a thermally insulated rod is kept at a temperature T_{1} and the other at T_{2} . The rod is composed of two sections of lengths L_{1} and L_{2} and thermal conductivities k_{1} and k_{2} respectively. The temperature at the interface of the sections is$ (1) $\frac{( K _{2} L _{2} T _{1} + K _{1} L _{1} T _{2} )}{( K _{1} L _{1} + K _{2} L _{2} )}$ (2) $\frac{( K _{2} L _{1} T _{1} + K _{1} L _{2} T _{2} )}{( K _{2} L _{1} + K _{1} L _{2} )}$ (3) $\frac{( K _{1} L _{2} T _{1} + K _{2} L _{1} T _{2} )}{( K _{1} L _{2} + K _{2} L _{1} )}$ (4) $\frac{( K _{1} L _{1} T _{1} + K _{2} L _{2} T _{2} )}{( K _{1} L _{1} + K _{2} L _{2} )}$ 168. $Temperature difference of 120^{\circ} C is maintained between two ends of a uniform rod AB of length 2 L . Another bent PQ of same cross-section as AB and length \frac{3 L}{2} is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:$ (1) $45^{\circ} C$ (2) $75^{\circ} C$ (3) $60^{\circ} C$ (4) $35^{\circ} C$ 169. $A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat ‘Q’ flows only from left to right through the blocks. Then in steady state$ (1) $heat flow through A and E slabs are same$ (2) $heat flow through slab E is maximum$ (3) $temperature difference across slab E is smallest$ (4) $heat flow through C = heat flow through B + heat flow through D.$ 170. $A hot liquid is kept in a big room. Its temperature is plotted as a function of time. Which of the following curves may represent the plot?$ (1) $a$ (2) $c$ (3) $d$ (4) $b$ 171. $Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length \frac{3 L}{2}, is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to:$ (1) $75°C$ (2) $45°C$ (3) $60°C$ (4) $35°C$ 172. $A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is U_{1}, between 999 nm and 1000 nm is U_{2} and between 1499 nm and 1500 nm is U_{3} . The Wien's constant b = 2.88 \times 1 0^{6} nmK . Then$ (1) $U_{1} = 0$ (2) $U_{3} = 0$ (3) $U_{1} > U_{2}$ (4) $U_{2} > U_{1}$ 173. $The adjoining diagram shows the spectral energy density distribution E_{λ} of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is$ (1) $32,000 K$ (2) $16,000 K$ (3) $8,000 K$ (4) $4,000 K$ 174. $Which of the following is the v_{m} -T graph for a perfectly black body$ (1) $A$ (2) $B$ (3) $C$ (4) $D$ 175. $A slab of stone of area 0.36 m^{2} and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is: (Given latent heat of fusion of ice = 3.36 \times 1 0^{5} J k g^{-1}):$ (1) $1.24 J/m/s/°C$ (2) $1.29 J/m/s/°C$ (3) $2.05 J/m/s/°C$ (4) $1.02 J/m/s/°C$ 176. $If a metallic sphere gets cooled from 6 2^{\circ} C to 5 0^{\circ} C in 10 minutes and in the next 10 minutes gets cooled to 4 2^{\circ} C, then the temperature of the surroundings is$ (1) $3 0^{o} C$ (2) $3 6^{o} C$ (3) $2 6^{o} C$ (4) $2 0^{o} C$ 177. $Hot water cools from 6 0^{o} C to 5 0^{o} C in the first 10 minutes and to 4 2^{o} C in the next 10 minutes. The temperature of the surrounding is$ (1) $5^{o} C$ (2) $1 0^{o} C$ (3) $1 5^{o} C$ (4) $2 0^{o} C$ 178. $Two identical beakers A and B contain equal volumes of two different liquids at 60^{\circ} C each and left to cool down. Liquid in A has density of 8 \times 10^{2} kg / m^{3} and specific heat of 2000 J kg^{- 1} K^{- 1} while liquid in B has density of 10^{3} kgm^{- 3} and specific heat of 4000 J kg^{- 1} K^{- 1} . Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)$ (1) (2) (3) (4) 179. $M grams of steam at 100^{\circ} C is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40^{\circ} C [heat of vaporization of water is 540 cal / g and heat of fusion of ice is 80 cal / g], the value of M is$ 180. $Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 1 0^{4} times the power emitted from B. The ratio (\frac{λ _{A}}{λ _{B}}) of their wavelengths λ_{A} and λ_{B} at which the peaks occur in their respective radiation curves is:$