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
JEE MAIN 2021, Medium
Download our app for free and get started
(b) In series ${R_{eq}} = {R_1} + {R_2}$
==> $\frac{{2l}}{{{K_{eq}}A}} = \frac{l}{{{K_1}A}} + \frac{l}{{{K_2}A}}$
==> $\frac{2}{{{K_{eq}}}} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}}$
==> ${K_{eq}} = \frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
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 long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?View Solution
- 2Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time isView Solution
- 3View SolutionIf the initial temperatures of metallic sphere and disc, of the same mass, radius and nature are equal, then the ratio of their rate of cooling in same environment will be
- 4A solid copper cube of edges $1\;cm$ is suspended in an evacuated enclosure. Its temperature is found to fall from ${100^o}C$ to ${99^o}C$ in $100\;s$. Another solid copper cube of edges $2\;cm$, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from ${100^o}C$ to ${99^o}C$ will be approximately ...... $\sec$View Solution
- 5The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m ^{2}$. It contains $300 g$ of a mixture of coal, wood and leaves with calorific value of $30 \,kJ / g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ} C$ and the room temperature is $0^{\circ} C$. Then, a reasonable estimate for the duration $t$ (in h) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body)View Solution
- 6View SolutionMode of transmission of heat, in which heat is carried by the moving particles, is
- 7If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$ , then the ratio of the radiant energy received on the earth to what it was previously will beView Solution
- 8View SolutionNewton's law of cooling is a special case of
- 9If $K_{1}$ and $K_{2}$ are the thermal conductivities $L_{1}$ and $L _{2}$ are the lengths and $A _{1}$ and $A _{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$.View Solution
Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be ........... $^{\circ} C$
- 10View SolutionFor cooking the food, which of the following type of utensil is most suitable