Compliance

Q. Which of the following are $\text{correct}$ for organisms that cause red tide?
(a) Stiff cellulosic plates on outer surface of wall
(b) Releases toxins
(c) Have photosynthetic pigments
(d) Found in fresh water only

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 ${100}^{\circ }C,{50}^{\circ }C$ and ${20}^{\circ }C$. The temperature of their junction is

1. ${60}^{\circ }C$
2. ${70}^{\circ }C$
3. ${50}^{\circ }C$
4. ${35}^{\circ }C$

Q. A cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at two different temperatures. 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

1. $k_1+k_2$
2. $\frac{k_1{k}_2}{(k_1+k_2)}$
3. $\frac{(k_1+3k_2)}{4}$
4. $\frac{(3k_1+k_2)}{4}$

Q. Read the following statements and select the $\text{correct}$ option.
$\text{StatementA}$ : Some marine dinoflagellates show bioluminescence.
$\text{Statement B:}$ $Gonyaulax$ produce a toxin into the sea water.

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 ${36}^{\circ }C$. The temperature difference across the layer $A$ is

1. $6^{\circ }C$
2. ${12}^{\circ }C$
3. ${18}^{\circ }C$
4. ${24}^{\circ }C$

Q. The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in figure, what will be the temperature at the junction of copper and steel?

1. ${75}^{\circ }\text{C}$
2. ${67}^{\circ }\text{C}$
3. ${33}^{\circ }\text{C}$
4. ${25}^{\circ }\text{C}$

Q. The container $A$ contains ice at $0^{\circ }\text{C}$. A conducting uniform rod $PQ$ of length $4R$ is used to transfer heat to the ice in the container. The end $P$ of the rod is maintained at ${100}^{\circ }\text{C}$ and the other end $Q$ is kept inside the container $A$. The complete ice melts in $23\text{minutes}$. In another experiments, two conductors in the shape of quarter circles of radii $2R$ and $R$ are welded to the conductor $PQ$ at $M$ and $N$ respectively and their other ends are inserted inside the container $A$. All conductors are made of the same material and have the same cross sectional area. Once again, the end $P$ is maintained at ${100}^{\circ }\text{C}$ and this time, the complete ice melts in $t\text{minutes}$. Find $t$.
[Assume no heat loss from the curved surface of the rods and take $\pi \simeq 3.0$]

1. $35\text{min}$
2. $21\text{min}$
3. $17.5\text{min}$
4. $12\text{min}$

Q. Thermal conductivity of the conductor shown in the figure is $0.92{\text{cal/cm s}}^{\circ }\text{C}$. Find the thermal resistance between points $P$ and $Q$ (in ${\text{s}}^{\circ }\text{C/cal}$).

1. $0.036$
2. $0.018$
3. $0.072$
4. $1$

Q. Five identical rods are joined as shown in figure. Point A and C are maintained at temperature ${120}^{\circ }C$ and ${20}^{\circ }C$, respectively. The temperature of junction B will be

1. ${100}^{\circ }C$
2. ${80}^{\circ }C$
3. ${70}^{\circ }C$
4. $0^{\circ }C$

Q. Two slabs each of area $A$, length $2\text{m}$ and $4\text{m}$, thermal conductivities $k_1=300{\text{W/m}}^{\circ }\text{C}$ and $k_2=200{\text{W/m}}^{\circ }\text{C}$ respectively are joined to form a single slab of length $6\text{m}$. Find the equivalent thermal conductivity of resultant slab. (in ${\text{W/m}}^{\circ }\text{C}$)

1. $300$
2. $225$
3. $325$
4. $275$

Q. Two sheets of thickness $d$ and $3d$, are in contact with each other. The temperature just outside the thinner sheet is $T_1$ and thicker sheet is $T_3$ as shown in figure. The temperature $T_1,T_2$ and $T_3$ are in arithmetic progression such that $T_1>T_3$. The ratio of thermal conductivity of thinner sheet to thicker sheet is

1. $1:3$
2. $3:1$
3. $2:3$
4. $2:9$

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

1. $16$
2. $32$
3. $64$
4. $40$

Q. A solid cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K_2.$ 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:

1. $\frac{4K_1+3K_2}{4}$
2. $\frac{3K_1+4K_2}{4}$
3. $\frac{3K_1+K_2}{4}$
4. $\frac{K_1+3K_2}{4}$

Q. Statement 1 : Equivalent thermal conductivity of two rods of same physical dimensions and having same thermal conductivity $\left(k\right)$ connected to each other in parallel combination is equal to $k$.
Statement 2 : Equivalent thermal conductivity of two rods of same physical dimensions and having same thermal conductivity $\left(k\right)$, connected to each other in series combination is equal to $k$.

1. Statement 1 is true but statement 2 is false.
2. Statement 2 is true but statement 1 is false.
3. Both statement 1 and statement 2 are true.
4. Both statement 1 and statement 2 are false.

Q. The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40\text{W}$ in the arrangement (a). Find the rates of heat flow when the rods are joined as in arrangement (b). (Assume $k_{Al}=200\text{W/m}{}^{\circ }\text{C}$ and $k_{Cu}=400\text{W/m}{}^{\circ }\text{C}$)

1. $75\text{W}$
2. $200\text{W}$
3. $400\text{W}$
4. $4\text{W}$

Q. Two metal rods $1$ and $2$ of same lengths have the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$, and cross-sectional areas $A_1$ and $A_2$ respectively. If the rate of heat conduction in $1$ is four times that in $2$, then

1. $K_1{A}_1=K_2{A}_2$
2. $K_1{A}_1=4K_2{A}_2$
3. $K_1{A}_1=2K_2{A}_2$
4. $4K_1{A}_1=K_2{A}_2$

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

1. Along $cd$
2. Along $lm$
3. Along $ab$
4. All the directions have equal thermal resistance

Q. The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40\text{W}$ in the arrangement (a). Find the rate of heat flow when the rods are joined as in the arrangement shown in (b).
[Assume $K_{Al}=200{\text{W/m}}^{\circ }\text{C}$ and $K_{cu}=400{\text{W/m}}^{\circ }\text{C}$]

1. $75\text{W}$
2. $400\text{W}$
3. $180\text{W}$
4. $4\text{W}$

Q. Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ }\text{C}$ and ${90}^{\circ }\text{C}$ respectively as shown. The temperature of junction of the three rods will be

1. ${45}^{\circ }\text{C}$
2. ${60}^{\circ }\text{C}$
3. ${30}^{\circ }\text{C}$
4. ${20}^{\circ }\text{C}$

Q. A wire consists of two layers as shown in the figure. Thermal conductivity of inner core of radius $2\text{cm}$ is $k$ and of the outer one of radius $4\text{cm}$ is $2k$. Find the equivalent thermal conductivity between its two ends $a$ and $b\left(k_{\text{eq}}\right)$.

1. $\frac{7k}{2}$
2. $\frac{7k}{8}$
3. $\frac{7k}{4}$
4. $\frac{5k}{4}$

Q. A spherical body of radius $b=\frac{4}{\pi }\text{m}$ has a concentric cavity of radius $a=\frac{2}{\pi }\text{m}$ as shown. Thermal conductivity of the material is $100{\text{W/m}}^{\circ }\text{C}$. Find the thermal resistance between inner and outer surface.

1. ${6.25\times {10}^{-4}}^{\circ }\text{C/W}$
2. ${1.25\times {10}^{-4}}^{\circ }\text{C/W}$
3. ${6.5\times {10}^{-4}}^{\circ }\text{C/W}$
4. ${3.75\times {10}^{-4}}^{\circ }\text{C/W}$

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

1. $500$
2. $250$
3. $300$
4. $350$