A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is
A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is
- [JEE MAIN 2019]
- A
$\frac{{{K_1} + {K_2}}}{2}$
- B
$K_1 + K_2$
- C
$\frac{{2{K_1} + {3K_2}}}{5}$
- D
$\frac{{{K_1} + {3K_2}}}{4}$
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The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio $1 : 2$ and their lengths are in the ratio $2 : 1$ . If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be
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- [JEE MAIN 2014]
Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is
Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is
An 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 figure
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.
An 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 figure
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.
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Assertion : The equivalent thermal conductivity of two plates of same thickness in contact is less than the smaller value of thermal conductivity.
Reason : For two plates of equal thickness in contact the equivalent thermal conductivity is given by : $\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}}$
Assertion : The equivalent thermal conductivity of two plates of same thickness in contact is less than the smaller value of thermal conductivity.
Reason : For two plates of equal thickness in contact the equivalent thermal conductivity is given by : $\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}}$
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