$A$ wall is made up of two layers $A$ and $B$ . The thickness of the two layers is the same, but materials are different. The thermal conductivity of $A$ is double than that of $B$ . In thermal equilibrium the temperature difference between the two ends is ${36^o}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^oC$
IIT 1980, Diffcult
Download our app for free and get started
(b) Suppose thickness of each wall is $x$ then ${\left( {\frac{Q}{t}} \right)_{combination}} = {\left( {\frac{Q}{t}} \right)_A}$
==> $\frac{{{K_S}A({\theta _1} - {\theta _2})}}{{2x}} = \frac{{2KA({\theta _1} - \theta )}}{x}$
$\because {K_S} = \frac{{2 \times 2K \times K}}{{(2K + K)}} = \frac{4}{3}K$ and $({\theta _1} - {\theta _2}) = 36^\circ $
==> $\frac{{\frac{4}{3}KA \times 36}}{{2x}} = \frac{{2KA({\theta _1} - \theta )}}{x}$
Hence temperature difference across wall $A$ is $({\theta _1} - \theta ) = {12^o}C$
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 is at a temperature $300 K$ . It emits energy at a rate, which is proportional toView Solution
- 2For the figure shown, when arc $ACD$ and $ADB$ are made of same material, the heat carried between $A$ and $B$ is $H$ . If $ADB$ is replaced with another material, the heat carried becomes $2H$ . If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$ , what is the ratio of the new conductivity to the old one of $ADB$View Solution
- 3A beaker full of hot water is kept in a room. If it cools from $80^{\circ} C$ to $75^{\circ} C$ in $t_1$, minutes, from $75^{\circ} C$ to $70^{\circ} C$ in $t_2$ minutes and from $70^{\circ} C$ to $65^{\circ} C$ in $t_3$ minutes, thenView Solution
- 4Distance between sun and Earth is $2 \times 10^{8}\, km ,$ temperature of sun $6000\, K ,$ radius of sun $7 \times 10^{5}\, km .$ If emmisivity of the earth is $0.6,$ find out the temperature of the earth in thermal equilibrium (in $k$)View Solution
- 5If the temperature of the body is increased by $10\% $ , the percentage increase in the emitted radiation will be ....... $\%$View Solution
- 6A cup of tea cools from $65.5^o C to 62.5 ^o C$ in one minute in a room of $22.5 ^o C$. How long will the same cup of tea take, in.............. minutes, to cool from $46.50^o C to 40.5 ^o C$ in the same room ? (choose nearest value)View Solution
- 7View SolutionIf a liquid is heated in weightlessness, the heat is transmitted through
- 8Two spheres $P$ and $Q$, of same colour having radii $8\;cm$ and $2\;cm$ are maintained at temperatures ${127^o}C$ and ${527^o}C$ respectively. The ratio of energy radiated by $P$ and $Q$ isView Solution
- 9The maximum energy in the thermal radiation from a hot source occurs at a wavelength of $11 \times {10^{ - 5}}cm$. According to Wein's law, the temperature of the source (on Kelvin scale) will be $n$ times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is $5.5 \times {10^{ - 5}}cm$. The value $n$ isView Solution
- 10Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition isView Solution