Title 14. Transmission of Heat Med.pdf ✅

1. The heat is flowing through a rod of length 50 cm and area of cross-section 5cm2 . Its ends are respectively at 250C and 1250C. The coefficient of thermal conductivity of the material of the rod is 0.092 kcal/m×s×0C. The temperature gradient in the rod is (a) 2 0C / cm (b) 2 0C / m (c) 20 0C / cm (d) 10 0C /m 2. Consider two rods of same length and different specific heats (s1 and s2), conductivities K1 and K2 and areas of cross-section (A1 and A2) and both giving temperature T1 and T2 at their ends. If the rate of heat loss due to conduction is equal, then (a) K1A1 = K2A2 (b) K2A1 = K1A2 (c) 2 2 2 1 1 1 s K A s K A = (d) 1 1 2 2 2 1 s K A s K A = 3. Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross- section of a semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is (a) 2 :  (b) 1 : 2 (c)  : 2 (d) 3 : 2 4. For cooking the food, which of the following type of utensil is most suitable (a) High specific heat and low conductivity (b) High specific heat and high conductivity (c) Low specific heat and low conductivity (d) Low specific heat and high conductivity 5. A heat flux of 4000 J/s is to be passed through a copper rod of length 10 cm and area of cross-section 100 cm2 . The thermal conductivity of copper is 400 W/m0C. The two ends of this rod must be kept at a temperature difference of (a) 1 0C (b) 10 0C (c) 100 0C (d) 1000 0C 6. The coefficients of thermal conductivity of copper, mercury and glass are respectively Kc, Km and Kg such that Kc> Km> Kg. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are respectively Xc, Xm and Xg then (a) Xc= Xm = Xg (b) Xc>Xm>Xg (c) Xc1 A Straightrod B
shown in figure In the steady state temperatures of outer surfaces are 1 and 2 . The temperature of common surface is– (a) 1 1 1 2 2 2 1 1 2 2 + + K d K d K d K d   (b) 1 1 2 2 1 2 K K K K   + + (c) 1 1 2 2 1 2 K K     + + (d) 1 1 2 2 2 1 1 2 2 1 K d K d K d K d   + + 14. Which of following qualities suit for a cooking utensil? (a) High specific heat and low thermal conductivity (b) High specific heat and high thermal conductivity (c) Low specific heat and low thermal conductivity (d) Low specific heat and high thermal conductivity 15. The lengths and radii of two rods made of same material are in the ratios 1 : 2 and 2 : 3 respectively; If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio: (a) 1 : 3 (b) 4 : 3 (c) 8 : 9 (d) 3 : 2 16. Two rods having thermal conductivities in the ratio of 5 : 3 and having equal length and equal cross-section are joined by face to face(series combination). If the temperature of free end of first rod is 100oC and the free end of second rod is 20oC, then temperature of the junction, is– (a) 50oC (b) 70oC (c) 85oC (d) 90oC 17. One end of a metal rod of length 1.0m and area of cross-section 100 cm2 is maintained at 100oC. If the other end of the rod is maintained at 0oC, the quantity of heat transmitted through the rod per minute will be (coefficient of thermal conductivity of materal of rod = 100W/mK) (a) 3 x 103 J (b) 6 x 103 J (c) 9 x 103 J (d) 12 x 103 J 18. The coefficients of thermal conductivity of a metal depends on (a) temperature difference between the two sides (b) thickness of the metal plate (c) area of the plate (d) none of the above 19. Two identical square rods of metal are welded end to end as shown in figure (a). Assume that 10 cal of heat flows through the rods in 2 min. Now the rods are welded as shown in figure. (b) The time it would take for 10 cal to flow through the rods now, is (a) 0.75 min (b) 0.5 min (c) 1.5 min (d) 1 min 20. Area of cross-section of two rods of equal lengths are A1 and A2 and thermal conductivities are K1 and K2 . Specific heats are S1 and S2 . condition for equal heat flow is– (a) K1 = K2 (b) K1 S1 = K2 S2 (c) 1 2 1 1 2 2 K K A S A S = (d) K1A1 = K2A2 21. If two metallic plates of equal thickness, equal cross section area and thermal conductivities K1 and K2 are put together face to face (series combination) and a common plate is constructed, then the equivalent thermal conductivity of this plate will be- (a) 1 2 1 2 K K K K+ (b) 1 2 1 2 2K K K K+ (c) 2 2 3/ 2 1 2 1 2 ( ) K K K K + (d) 2 2 3/ 2 1 2 1 2 ( ) 2 K K K K + 22. Consider a compound slab consisting of two different materials having equal thicknesses, equal cross section area and thermal conductivities k and 2k respectively. If they are connected in parallel combination, the equivalent thermal conductivity of the slab is– K1 K2 d1 d2 0°C 100°C (a)
(a) 2 (b) 3k (c) 2 3k (d) 2 3 k 23. The two ends of a rod of length L and a uniform cross-sectional area A kept at two temperatures T1 and T2 (T1 >T2 ). The rate of heat transfer, dQ dt , through the rod in a steady state is given by (a) dQ dt = 1 2 KL T T ( ) A − (b) 1 2 dQ K T T ( ) dt LA − = (c) 1 2 ( ) dQ KLA T T dt = − (d) 1 2 dQ KA T T ( ) dt L − = 24. A square is made of four rods of same material one of the diagonal of a square is at temperature difference 100°C, then the temperature difference of second diagonal : (a) 0°C (b) 100 (c) 100 2 (d) 100°C 25. Three rods made of the same material and having the same cross-section are joined as shown in the fig. Each rod is of same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be : (a) 45°C (b) 60°C (c) 30°C (d) 20°C 26. Two containers, one is having ice at 0°C and other containing boiling water at 100°C are connected by two identical rods. When rods are in parallel the rate of heat transfer is Q1 and when rods are in series, the rate of heat transfer is Q2 . Then Q2 /Q1 will be : (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4 27. 2 litre water at 27°C is heated by a 1 kW heater in an open container. On an average heat is lost to surroundings at the rate 160 J/s. The time required for the temperature to reach 77°C is (a) 8 min 20 sec (b) 10 min (c) 7 min (d) 14 min 28. If the temperature difference on the two sides of a wall increases from 100°C to 200°C, its thermal conductivity (a) remains unchanged (b) is doubled (c) is halved (d) becomes four times 29. A cylindrical rod having temperature T1 and T2 at its ends. The rate of flow of heat is Q1 cal/sec. If all the linear dimensions are doubled keeping temperature constant then rate of flow of heat Q2 will be– (a) 4Q1 (b) 2Q1 (c) 1 4 Q (d) 1 2 Q 30. One end of a thermally insulated rod is kept at a temperature T1 and the other at T2 . The rod is composed of two sections of lengths L1 and L2 and thermal conductivities k1 and k2 respectively. The temperature at the interface of the sections is (a) 2 2 1 1 1 2 1 1 2 2 ( ) ( ) K L T K L T K L K L + + (b) 2 1 1 1 2 2 2 1 1 2 ( ) ( ) K L T K L T K L K L + + (c) 1 2 1 2 1 2 1 2 2 1 ( ) ( ) K L T K L T K L K L + + (d) 1 1 1 2 2 2 1 1 2 2 ( ) ( ) K L T K L T K L K L + + 31. Three rods A,B and C of same length and same cross-section area are joined as shown in the figure. Their thermal
conductivities are in the ratio 1 : 2 : 1.5. If the open ends of A and C are at 200°C and 18°C respectively, the temperature at the junction of A and B in equilibrium is- (a) 156°C (b) 116°C (c) 74°C (d) 148°C 32. In the above question, the temperature at the junction of B and C will be- (a) 124°C (b) 124°K (c) 74°C (d) 74°K 33. The ends of the two rods of different materials with their thermal conductivities, radii of cross-section and lengths in the ratio 1 : 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/sec., that in the shorter rod will be- (in cal/sec) (a) 1 (b) 2 (c) 8 (d) 16 34. The coefficients of thermal conductivity of copper, mercury and glass are respectively Kc , Km and Kg such that Kc > Km > Kg . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are Xc , Xm and Xg . (a) Xc = Xm = Kg (b) Xc > Xm > Xg (c) Xc < Xm < Xg (d) Xm < Xc < Xg 35. A compound slab is composed of two parallel layers of different material, with thicknesses 3 cm and 2 cm. The temperatures of the outer faces of the compound slab are maintained at 100°C and 0°C. If conductivities are 0.036 cal/cm-sec-°C and 0.016 cal/cm-sec- °C then the temperature of the junction is- (a) 40°C (b) 60°C (c) 100°C (d) 50°C 36. The intensity of heat radiation by a point source measured by a thermopile placed at a distance d is , If the distance of thermopoile is doubled then the intensity of radiation will be- (a)  (b) 2  (c) 4  (d) 2  37. Two rods of copper and brass of same length and area of cross- section are joined as shown. One end is kept at 100°C and the other at 0°C. The temperature at the mid-point will be- (a) more if A is at 100°C and B at 0°C (b) more if A is at 0°C and B at 100°C (c) will be same in both the above cases, but not 50°C (d) 50°C in both the above cases 38. Two identical square rods of metal are welded end to end as shown in fig. (a) 20 cal. of heat flows through it in 4 min. If the rods re welded as shown in fig. (b), the same amount of heat will flow through the rods in- (a) 1 min. (b) 2 min. (c) 3 min. (d) 16 min. 39. A wall consists of alternating blocks with length ‘d’ and coefficient of thermal conductivity k1 and k2 . The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is :- (a) K1 + K2 (b) 1 2 ( ) 2 K K+ (c) 1 2 1 2 K K K K+ (d) 1 2 1 2 2 K K K K+ 40. Five rods of same dimensions are arranged as shown in the fig. They have thermal conductivities, k1 , k2 , k5 , k4 and k3 when A B C 200oC K 2K 1.5K 18oC A Copper Brass B