Two identical square rods of metal are welded end to end as shown in figure $(i)$ , $20$ calories of heat flows through it in $4$ minutes. If the rods are welded as shown in figure $(ii)$, the same amount of heat will flow through the rods in ....... $\min.$
Medium
Download our app for free and get started
(a) $\frac{Q}{t} = \frac{{KA\,\Delta \theta }}{l}$$ = \frac{{\Delta \theta }}{{(l/KA)}} = \frac{{\Delta \theta }}{R}$ ( $R =$ Thermal resistance)
==> $t \propto R$ ( $Q$ and $\Delta \theta $ are same)
==> $\frac{{{t_P}}}{{{t_S}}} = \frac{{{R_P}}}{{{R_S}}} = \frac{{R/2}}{{2R}} = \frac{1}{4}$
==>${t_P} = \frac{{{t_S}}}{4} = \frac{4}{4} = 1\min .$
(Series resistance ${R_S} = {R_1} + {R_2}$ and parallel resistance ${R_P} = \frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$)
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 sphere at temperature $600\,K$ is placed in an environment of temperature is $200\,K$ . Its cooling rate is $H$ . If its temperature reduced to $400\,K$ then cooling rate in same environment will becomeView Solution
- 2A black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere, where $\alpha $ is a constant, then the time taken for the sphere to cool down to temperature $2T_0$ will be ( $\sigma $ is Stefan Boltzmann constant)View Solution
- 3Two metal spheres have radil $r$ and $2 r$ and they emit thermal radiation with maximum intensities at wavelengths $\lambda$ and $2 \lambda$ respectively. The respective ratio of the radiant energy emitted by them per second will be .........View Solution
- 4Two rods $A$ and $B$ of different materials are welded together as shown in figure.Their thermal conductivities are $K_1$ and $K_2$ The thermal conductivity of the composite rod will beView Solution
- 5If temperature of sun is decreased by $1 \%$ then the value of solar constant will change by ........... $\%$View Solution
- 6Two 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 isView Solution
- 7View SolutionFor cooking the food, which of the following type of utensil is most suitable
- 8View SolutionThe cause of Fraunhoffer lines is
- 9A wall consists of alternating blocks of length $d$ and coefficient of thermal conductivity $K_{1}$ and $K_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right isView Solution
- 10Two sheets of thickness $d$ and $3d$, are touching each other. The temperature just outside the thinner sheet side is $A$, and on the side of the thicker sheet is $C$. The interface temperature is $B. A, B$ and $C$ are in arithmetic progressing, the ratio of thermal conductivity of thinner sheet and thicker sheet isView Solution
