Wires $A$ and $B$ have identical lengths and have circular cross-sections. The radius of $A$ is twice the radius of $B$ $i.e.$ ${r_A} = 2{r_B}$. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by
Medium
Download our app for free and get started
(d) $\frac{Q}{t} = \frac{{KA\Delta \theta }}{l} \Rightarrow \frac{{{K_A}}}{{{K_B}}} = \frac{{{A_B}}}{{{A_A}}} = {\left( {\frac{{{r_B}}}{{{r_B}}}} \right)^2} = \frac{1}{4} \Rightarrow {K_A} = \frac{{{K_B}}}{4}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A black body at $227^o C$ radiates heat at the rate of $7\; cals/cm^2 s$. At a temperature of $727^o C$, the rate of heat radiated in the same units will beView Solution
- 2Two spheres of the same material have radii $1\ m$ and $4\ m$ and temperatures $4000\ K$ and $2000\ K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second isView Solution
- 3Two spheres of different materials one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting ice in the large radius one is $25$ minutes and that for smaller one is $16$ minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere isView Solution
- 4A body initially at $80^o C$ cools to $64^o C$ in $5$ minutes and to $52^o C$ in $10 $ minutes. The temperature of the body after $15$ minutes will be ...... $^oC$View Solution
- 5Four conducting rods are joined to make a square. All rods are identical and ends $A, B$ and $C$ are maintained at given temperatures. choose $INCORRECT$ statement for given arrangement in steady state. (value of $\frac {KA}{L}$ is $1\frac{J}{{{S^o}C}}$ , symbols , have their usual meaning)View Solution
- 6Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $ K$ and $2K$ respectively. The equivalent thermal conductivity of the slab isView Solution
- 7A cup of tea cools from $80\,^oC$ to $60\,^oC$ in one minute. The ambient temperature is $30\,^oC$. In cooling from $60\,^oC$ to $50\,^oC$, it will take ....... $\sec$View Solution
- 8Four spheres $A, B, C$ and $D$ are of same radius but made of different metals. Their densities are in ratio $6 : 3 : 4 : 5$ and specific heats are in ratio $2 : 5 : 4 : 6$ . These are initially kept at the same temperature and placed in the same surroundings. The sphere which has the slowest rate of cooling isView Solution
- 9The wavelength of maximum emitted energy of a body at $700 K$ is $4.08$ $\mu m$. If the temperature of the body is raised to $1400 K$ , the wavelength of maximum emitted energy will be ........ $\mu m$View Solution
- 10An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figureView Solution
In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.
In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.
In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.
In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.
