# Conduction Law

## Trending Questions

**Q.**A body cools in 7 min from 60∘ C to 40∘ C. What will be its temperature after the next 7 min ?

The temperature of surroundings is 10∘ C. [Assume Newton's Law of cooling is applicable]

- T=32∘ C
- T=28∘ C
- T=24∘ C
- T=36∘ C

**Q.**Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1and K2. The thermal conductivity of the composite rod will be

- K1+K22
- 3(K1+K2)2
- K1+K2
- 2(K1+K2)

**Q.**If K1 and K2 are the thermal conductivities, L1 and L2 are the lengths and A1 and A2 are the cross sectional areas of steel and copper rods respectively such that K2K1=9, A1A2=2, L1L2=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

**Q.**Two ends of a rod of non-uniform area of cross-section are maintained at temperature T1 and T2 (T1>T2) as shown in the figure. If I is the heat current through the cross - section of the conductor at distance x from its left face then the variation of I with time t is best represented by

**Q.**Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or II as shown in the figure. One of the blocks has thermal conductivity K and the other, 2K. The temperature difference between the ends along the x-axis is the same in both the configuarations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in configuration I. The time to transport the same amount of heat in the configuration II is:-

- 2.0 s
- 3.0 s
- 4.5 s
- 6.0 s

**Q.**A water cooler of storage capacity 120 litres can cool water at a constant rate of P. In a closed circulation system (as shown schematically in this figure), the water from the cooler is used to cool an external device that constantly generates 3 kW of power (thermal load). The temperature of the water fed into the device cannot exceed 30∘C and the entire 120 litres of water is initially cooled to 10∘C. The entire system is thermally insulated. The minimum value of P for which the device can be operated for 3 hours (taking the specific heat capacity of water =4.2 kJ kg−1K−1 and the density of water =1000 kg m−3) is

- 1600 W
- 2067 W
- 2533 W
- 3933 W

**Q.**The heat conduction equation dQdt=−kA(dTdx) applied for heat transfer through a plane slab presumes:

1. Steady- state one-dimensional conduction.

2. Constant value of thermal conductivity

3. The bounding surfaces are isothermal.

4. Temperature gradient is constant.

of these statements:-

- 2 and 4 are correct
- 1, 3 and 4 are correct
- 1 , 2 , and 3 are correct
- 2 , 3 , and 4 are correct

**Q.**A rod of length L and uniform cross-sectional area has varying thermal conductivity which changes linearly from 2K at end B to K at the other end A. The ends A and B of the rod are maintained at constant temperature 100∘C and 0∘C, respectively. At steady state, the graph of temperature : T=T(x) where x= distance from end A will be

**Q.**A hollow sphere of inner radius R and outer radius 2R is made of a material of thermal conductivity K. It is surrounded by another hollow sphere of inner radius 2R and outer radius 3R made of the same material of thermal conductivity K. The inside of the smaller sphere is maintained at 0∘C and the outside of the bigger sphere is at 100∘C. The system is in steady state. Find the temperature of the interface.

- 50∘C
- 100∘C
- 75∘C
- 125∘C

**Q.**Three rods of same material, same area of cross-section but different lengths 10 cm, 20 cm and 30 cm are connected at a point as shown in the figure. Find the temperature of junction ′O′.

- 19.2∘C
- 16.4∘C
- 11.5∘C
- 22∘C

**Q.**

Why does the heat transfer coefficient increase with velocity?

**Q.**Two identical square rods of metal are welded end to end as shown in figure (a), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in

- 1 minute
- 2 minutes
- 4 minutes
- 16 minutes

**Q.**The dimension of radiation pressure is -

- [ML1T2]
- [ML1T−2]
- [ML−1T2]
- [ML−1T−2]

**Q.**

A uniform slab of dimension 10 cm × 10 cm × 1 cm is kept between two heat reservoirs at temperatures 10∘C and 90∘C. The larger surface areas touch the reservoirs. The thermal conductivity of the material is 0.80Wm−1∘C−1 Find the amount of heat flowing through the slab per minute.

**Q.**If a liquid takes 30 s in cooling from 95∘C to 90∘C and 70 s in cooling from 55∘C to 50∘C then temperature of room is -

- 16.5∘C
- 22.5∘C
- 28.5∘C
- 32.5∘C

**Q.**The specific heat of a metal at low temperatures varies according to S=aT3 where a is a constant and T is absolute temperature. The heat energy needed to raise the temperature of unit mass of the metal from T=1 K to T=2 K is

- 15a4
- 2a3
- 12a5
- 3a

**Q.**

Steam at 120∘C is continuously passed through a 50 -cm long rubber tube of inner and outer radii 1.0 cm and 1.2 cm. The room temperature is 30∘C. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = 0.15Js−1m−1∘C−1.

**Q.**

In the relation P=αβ eαxnRθ, P is power, x is distance, n is number of moles, R is gas constant and θ is temperature. The dimensional formula of β is

[M0L0T0]

[M1L0T1]

[M0L−1T1]

[M0L−1T−1]

**Q.**Five identical rods are joined as shown in figure. Point A and C are maintained at temperature 120∘ C and 20∘ C respectively. The temperature of junction B will be

- C
- C
- C
- C

**Q.**A composite wall having three layers of thickness 0.3 m, 0.2 m and 0.1 m and of thermal conductivity 0.6, 0.4 and 0.1 W/m-K respectively, has a surface area of 1 m2. If the inner and outer temperatures of the composite wall are 1840 K and 340 K respectively, find the rate of heat transfer.

- 150 W
- 150 W
- 75 W
- 750 W

**Q.**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/m∘C. The two ends of the rod must be kept at temperature difference of

- 100∘C
- 1∘C
- 10∘C
- 1000∘C

**Q.**

Two plates of the same area and the same thickness having thermal conductivities k1 and k2 are placed one on top of the other. The top and bottom faces of the composite plate are maintained at different constant temperatures. The thermal conductivity of the composite plate will be

k1k2(k1+k2)

(k1+k2)

2k1k2(k1+k2)

12(k1+k2)

**Q.**

A pitcher with 1 -mm thick porous walls contains 10 kg of water. Water comes to its outer surface and evaporates at the rate of 0.1gs−1. The surface are aof the pitcher (one side) = 200 cm2. The room temperature = 42∘, latent heat of vaporization = 2.27×106Jkg−1, and the thermal conductivity of the porous walls = 0.80Js−1m−1∘C−1. Calculate the temperature of water in the pitcher when it attains a constant value.

**Q.**

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross -sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

**Q.**

The normal body-temperature of a person is 97∘F Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47∘F, surface of the body under clothes = 1.6m2, conductivity of the cloth = 0.04Js−1m−1∘C−1, thickness of the cloth = 0.5 cm.

**Q.**Four rods of same material but different radii r and length l are used to connect two reservoirs of heat at different temperatures. Which one will conduct heat fastest?

- r= 2 cm, l=0.5 m
- r= 1 cm, l=0.5 m
- r= 1 cm, l=1 m
- r= 2 cm, l=2 m

**Q.**Which of the following options is incorrect in reference to Fourier's law of heat conduction?

- Rate of heat flow is proportional to the cross-sectional area of rod
- Rate of heat flow is proportional is the temperature difference between the ends of the rod
- Rate of heat flow is inversely proportional to thickness of the rod
- Rate of heat flow is proportional to the coefficient of thermal conductivity of material of the rod

**Q.**

A cubical box of volume 216cm3 is made up of 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is 5∘C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

**Q.**Two walls of thickness d1 and d2, thermal conductivities K1 and K2 are in contact. In the steady state, if the temperature at the outer surfaces are T1 and T2, the temperature at the contact of the walls will be

- K1T1+K2T2d1+d2
- K1T1d2+K2T2d1K1d2+K2d1
- (K1d1+K2d2)T1T2T1+T2
- K1d1T1+K2d2T2K1d1+K2d2

**Q.**The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio 1:2 are maintained at the same temperature difference. If the rate of flow of heat in the longer rod is 4 cal/sec, then that in the shorter rod in cal/sec will be

- 1
- 8
- 16
- 2