A cylindrical rod with one end in a steam chamber and other end in ice results in melting of 0.1 gm

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10-2.Transmission of Heat

medium

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1$ gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in $gm/\sec $will be

$3.2$

$1.6$

$0.2$

$0.1$

Solution

$⇒$ $\frac{{mL}}{t}$ $ = \frac{{K(\pi {r^2})\Delta \theta }}{l}$

$⇒$ Rate of melting of ice $\left( {\frac{m}{t}} \right) \propto \frac{{K{r^2}}}{l}$
Since for second rod $K$ becomes $\frac{1}{4}th$ $r$ becomes double and length becomes half, so rate of melting will be twice i.e. ${\left( {\frac{m}{t}} \right)_2} = 2\,{\left( {\frac{m}{t}} \right)_1} = 2 \times 0.1 = 0.2\,gm/sec.$

Standard 11

Physics

A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ……….. $Wm^{-2}$

hard

(JEE MAIN-2019)

Four 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)

medium

Which of the following cylindrical rods will conduct most heat, when their ends are maintained at the same steady temperature

medium

Figure shows three different arrangements of materials $1, 2$ and $3$ to form a wall. Thermal conductivities are $k_1 > k_2 > k_3$ . The left side of the wall is $20\,^oC$ higher than the right side. Temperature difference $\Delta T$ across the material $1$ has following relation in three cases

easy

If two metallic plates of equal thicknesses and thermal conductivities ${K_1}$ and ${K_2}$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

medium

(JEE MAIN-2021)

Solution

Similar Questions

A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ……….. $Wm^{-2}$

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