Heat transfer - conduction, convection and radiation — practice questions

Question 1 · difficulty L2 · understanding

Two plates $$\mathrm{A}$$ and $$\mathrm{B}$$ have thermal conductivities $$84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ and $$126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $$\mathrm{A}$$ and $$\mathrm{B}$$ are kept at $$100^{\circ} \mathrm{C}$$ and $$0{ }^{\circ} \mathrm{C}$$ respectively, then the temperature of the surface of contact in steady state is _____________ $${ }^{\circ} \mathrm{C}$$.

Question 2 · difficulty L2 · understanding

The temperature of a body in air falls from $40^{\circ} \mathrm{C}$ to $24^{\circ} \mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ} \mathrm{C}$. The temperature of the body in the next 4 minutes will be :

• A. $\frac{28}{3}{ }^{\circ} \mathrm{C}$
• B. $\frac{56}{3}{ }^{\circ} \mathrm{C}$
• C. $\frac{42}{3}{ }^{\circ} \mathrm{C}$
• D. $\frac{14}{3}{ }^{\circ} \mathrm{C}$

Question 3 · difficulty L2 · understanding

On celcius scale the temperature of body increases by $$40^{\circ} \mathrm{C}$$. The increase in temperature on Fahrenheit scale is :

• A. $$75^{\circ} \mathrm{F}$$
• B. $$70^{\circ} \mathrm{F}$$
• C. $$72^{\circ} \mathrm{F}$$
• D. $$68^{\circ} \mathrm{F}$$

Question 4 · difficulty L2 · understanding

A body cools in 7 minutes from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$. The temperature of the surrounding is $$10^{\circ} \mathrm{C}$$. The temperature of the body after the next 7 minutes will be:

• A. $$34^{\circ} \mathrm{C}$$
• B. $$28^{\circ} \mathrm{C}$$
• C. $$32^{\circ} \mathrm{C}$$
• D. $$30^{\circ} \mathrm{C}$$

Question 5 · difficulty L2 · understanding

Two identical metal wires of thermal conductivities K 1 and K 2 respectively are connected in series. The effective thermal conductivity of the combination is :

• A. $${{2{K_1}{K_2}} \over {{K_1} + {K_2}}}$$
• B. $${{{K_1} + {K_2}} \over {{K_1}{K_2}}}$$
• C. $${{{K_1} + {K_2}} \over {2{K_1}{K_2}}}$$
• D. $${{{K_1}{K_2}} \over {{K_1} + {K_2}}}$$

Question 6 · difficulty L2 · understanding

The temperature $$\theta$$ at the junction of two insulating sheets, having thermal resistances R 1 and R 2 as well as top and bottom temperatures $$\theta$$ 1 and $$\theta$$ 2 (as shown in figure) is given by :

• A. $${{{\theta _1}{R_2} + {\theta _2}{R_1}} \over {{R_1} + {R_2}}}$$
• B. $${{{\theta _1}{R_1} + {\theta _2}{R_2}} \over {{R_1} + {R_2}}}$$
• C. $${{{\theta _1}{R_2} - {\theta _2}{R_1}} \over {{R_2} - {R_1}}}$$
• D. $${{{\theta _2}{R_2} - {\theta _1}{R_1}} \over {{R_2} - {R_1}}}$$

Question 7 · difficulty L2 · understanding

A body cools from $$80^{\circ} \mathrm{C}$$ to $$60^{\circ} \mathrm{C}$$ in 5 minutes. The temperature of the surrounding is $$20^{\circ} \mathrm{C}$$. The time it takes to cool from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$ is :

• A. 500 s
• B. $$\frac{25}{3} \mathrm{~S}$$
• C. 450 s
• D. 420 s

Question 8 · difficulty L2 · understanding

A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will take to cool from 75$$^\circ$$C to 69$$^\circ$$C?

• A. 2 minutes
• B. 0.5 minute
• C. 1.4 minutes
• D. 1 minute

Question 9 · difficulty L2 · understanding

A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the body to cool from 51$$^\circ$$ C to 49$$^\circ$$ C is :

• A. 4 min.
• B. 3 min.
• C. 8 min.
• D. 6 min.

Question 10 · difficulty L2 · understanding

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS. Column I Column II (A) Bimetallic strip (P) Radiation from a hot body (B) Steam engine (Q) Energy conversion (C) Incandescent lamp (R) Melting (D) Electric fuse (S) Thermal expansion

• A. $$[\mathrm{A} \rightarrow(\mathrm{Q, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]$$
• B. $$[\mathrm{A} \rightarrow(\mathrm{R, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R, S})]$$
• C. $$[\mathrm{A} \rightarrow(\mathrm{S}); \mathrm{B} \rightarrow(\mathrm{Q}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]$$
• D. $$[\mathrm{A} \rightarrow(\mathrm{P, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]$$