A hollow copper sphere $S$ and a hollow copper cube $ C$ , both of negligible thin walls of same area, are filled with water at $90°C$ and allowed to cool in the same environment. The graph that correctly represents their cooling is
Diffcult
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(c)$\frac{{d\theta }}{{dt}} = \frac{{\varepsilon A\sigma }}{{mc}}4\theta _0^3\Delta \theta $
For given sphere and cube $\frac{{\varepsilon A\sigma }}{{mc}}4\theta _0^3\Delta \theta $ is constant so for both rate of fall of temperature $\frac{{d\theta }}{{dt}} = $constant
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One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$ . The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is
A hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of same material of thermal conductivity $K$. The inside of smaller sphere is maintained at $0^o C$ and the outside of bigger sphere at $100^o C$. The system is in steady state. The temperature of the interface will be ........ $^oC$
A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 K$. At time $t =0$, the temperature of the object is $200 K$. The temperature of the object becomes $100 K$ at $t = t _1$ and $50 K$ at $t = t _2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $\left( t _2 / t _1\right)$ is. . . . .
A black body of surface area $10cm^2$ is heated to $127°C$ and is suspended in a room at temperature $27°C$ . The initial rate of loss of heat from the body at the room temperature will be ...... $W$
A room is maintained at ${20^o}C$ by a heater of resistance $20$ ohm connected to $200$ volt mains. The temperature is uniform through out the room and heat is transmitted through a glass window of area $1{m^2}$ and thickness $0.2$ cm. What will be the temperature outside ....... $^oC$ ? Given that thermal conductivity $K=0.2$ for glass is and $J = 4.2 J/cal$
A body initially at $80^o C$ cools to $64^o C$ in $5$ minutes and to $52^o C$ in $10 $ minutes. The temperature of the body after $15$ minutes will be ...... $^oC$
Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T\ K$, evaluate the total radiant powerd incident of Earth at a distance $r$ from the Sun
Where $r_{0}$ is the radius of the earth and $\sigma$ is Stefan's constant.
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} - {T_1})K}}{x}} \right)f$, with $f $ which equal to