# Thermal Resistance

## Trending Questions

**Q.**Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be

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

**Q.**A wooden bowl conducts less heat than a copper bowl because

- kWood>kCopper
- kWood≤kCopper
- kWood=kCopper
- kWood<kCopper

**Q.**A wall has two layers A and B, each made of different materials. Both the layers have the same thickness and cross secional area. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36∘C. The temperature difference across the layer A is

- 6∘C
- 12∘C
- 18∘C
- 24∘C

**Q.**A hollow cylindrical pipe of length 10 cm has inner radius r1=3 cm and outer radius r2=12 cm. The temperature difference between the inner and outer layer of cylindrical pipe is 100∘C and the thermal conductivity of cylindrical pipe is 150 W/m∘C. Find the rate of heat transfered (in kW) between inner and outer layers.

(Take ln2=0.693)

- 3.4
- 6.8
- 10
- 13.6

**Q.**Figure shown below represents, parallel combination of two metallic slabs of same thickness having area of cross sections 2 m2 and 3 m2 respectively, connected to the same temperature difference. If the thermal conductivities of each slab is 300 W/m∘C, then equivalent thermal conductivity is (in W/m∘C)

- 500
- 250
- 300
- 350

**Q.**Three rods of the same dimension have thermal conductivities 3K, 2K and K. They are arranged as shown in figure given below, with their ends at 100∘C, 50∘C and 20∘C. The temperature of their junction is

- 60∘C
- 70∘C
- 50∘C
- 35∘C

**Q.**Two sheets of thickness d and 3d, are in contact with each other. The temperature just outside the thinner sheet is T1 and thicker sheet is T3 as shown in figure. The temperature T1, T2 and T3 are in arithmetic progression such that T1>T3. The ratio of thermal conductivity of thinner sheet to thicker sheet is

- 1:3
- 3:1
- 2:3
- 2:9

**Q.**Two rods having same length and cross-sectional area are connected individually between temperature T1 and T2. If the rate of loss of heat due to condution is equal and specific heat of two rods are in the ratio 1:2, then the ratio of their thermal conductivity will be

- 1:1
- 1:2
- 2:1
- 1:√2

**Q.**In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature θ is

- 200∘ C
- 60∘ C
- 75∘ C
- 80∘ C

**Q.**A solid cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. If 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:

- 4K1+3K24
- 3K1+4K24
- 3K1+K24
- K1+3K24

**Q.**The diagram shown below represents a slab of conductivity K. Find the direction along which the thermal resistance is maximum.

- Along cd
- Along lm
- Along ab
- All the directions have equal thermal resistance

**Q.**

Three rods of material x and three of material y are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end A is maintained at 60∘C and the junction E at 10 ∘ C, calculate the temperature of the junction B. The thermal conductivity of x is 800 W/M- ∘ C and

that of y is 400 W/M- ∘ C

50∘C

20∘C

60∘C

40∘C

**Q.**Four rods of same material having the same cross section and length have been joined as shown. The temperature of the junction of the rods will be

- 20∘C
- 30∘C
- 45∘C
- 60∘C

**Q.**Thermal conductivity of the conductor shown in the figure is 0.92 cal/cm s∘C. Find the thermal resistance between points P and Q (in s∘C/cal).

- 0.036
- 0.018
- 0.072
- 1

**Q.**Two metal rods 1 and 2 of same lengths have the same temperature difference between their ends. Their thermal conductivities are K1 and K2, and cross-sectional areas A1 and A2 respectively. If the rate of heat conduction in 1 is four times that in 2, then

- K1A1=K2A2
- K1A1=4K2A2
- K1A1=2K2A2
- 4K1A1=K2A2

**Q.**Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be

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

**Q.**Four rods of silver, copper, brass and wood are of same shape. They are heated together after wrapping a paper on it, the paper will burn first on

- Silver
- Copper
- Brass
- Wood

**Q.**The net thermal resistance of two identical rods connected in series is greater than that of resistance offered by each rod individually.

- False
- True

**Q.**

Find the heat current, i.

- (K1K2Al1K2+l2K1)ΔT
- (K1K2Al2K2+l1K1)ΔT
- (K1Al1+l2)ΔT
- (K21K22Al1K22+l2K21)ΔT

**Q.**A spherical body of radius b=4π m has a concentric cavity of radius a=2π m as shown in the figure. Thermal conductivity of the material is 100 W/m∘C. If temperature of inner surface is kept at 70∘C and of the outer surface at 30∘C, then find the rate of heat flow. (in kW)

- 16
- 32
- 64
- 40

**Q.**

Find the Requivalent.

- R1
- R2
- R1+R2
- R1R2R1+R2

**Q.**Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown in the figure, with their ends at 100∘C, 50∘C and 0∘C. The temperature of their junction point is:

- 75∘C
- 2003∘C
- 40∘C
- 1003∘C

**Q.**For the figure shown below, choose the option that correctly represents the combination.

- K1 and K2 are in series combination and together they are in parallel combination with K3.
- K1 and K2 are in parallel combination and together they are in series combination with K3.
- K1, K2 and K3 all are in parallel combination with each other.
- K1, K2 and K3 all are in series combination with each other.

**Q.**A metallic cylindrical vessel whose inner and outer radii are r1 and r2 is filled with ice at 0∘C. The mass of the ice in the cylinder is m. Circular surfaces of the cylinder are sealed completely with adiabatic walls. The vessel is kept in air and the temperature of the air is 50∘C. How long will it take for the ice to melt completely?

[Thermal conductivity of the cylinder is K and its length is l. Latent heat of fusion of ice is L].

- mL50πKlln(r1r2)
- mL200πKlln(r1r2)
- mLln(r2r1)100πKl
- mLln(r2r1)50πKl

**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

- 100∘C
- 80∘C
- 70∘C
- 0∘C

**Q.**Two ends of a conducting rod of varying cross-section are maintained at 200∘C and 0∘C respectively. In staedy state

- temperature difference across AB and CD are equal
- temperature difference across AB is greater than that of across CD
- temperature difference across AB is less than that of across CD
- temperature difference may be equal or different depending on the thermal conductivity of the rod

**Q.**A spherical body of radius b=4π m has a concentric cavity of radius a=2π m as shown. Thermal conductivity of the material is 100 W/m∘C. Find the thermal resistance between inner and outer surface.

- 6.25×10−4∘C/W
- 1.25×10−4∘C/W
- 6.5×10−4∘C/W
- 3.75×10−4∘C/W

**Q.**A metallic cylindrical vessel whose inner and outer radii are r1 and r2 is filled with ice at 0∘C. The mass of the ice in the cylinder is m. Circular surfaces of the cylinder are sealed completely with adiabatic walls. The vessel is kept in air and the temperature of the air is 50∘C. How long will it take for the ice to melt completely?

[Thermal conductivity of the cylinder is K and its length is l. Latent heat of fusion of ice is L].

- mL50πKlln(r1r2)
- mL200πKlln(r1r2)
- mLln(r2r1)100πKl
- mLln(r2r1)50πKl

**Q.**Two identical conducting rods are first connected independently to two vessels, one containing water at 100∘C and the other containing ice at 0∘C. In the second case, the rods are joined end to end and connected to the same vessels. Let q1 and q2 gram per second be the rate of melting of ice in the two cases respectively. The ratio q1q2 is

- 12
- 2
- 4
- 14

**Q.**Thermal conductivity of the conductor shown in the figure is 0.92 cal/cm s∘C. Find the thermal resistance between points P and Q (in s∘C/cal).

- 0.036
- 0.018
- 0.072
- 1