Heat Transfer
A 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)
Heat Transfer
A spherical black body with a radius of $$12\ cm$$ radiates $$450\ W$$ power at $$500\ K$$. If the radius were halved and the temperature doubled, the power radiated in watt would be:
Heat Transfer
Two spherical stars $$A$$ and $$B$$ emit blackbody radiation. The radius of $$A$$ is $$400$$ times that of $$B$$ and $$A$$ emits 10$$^4$$ times the power emitted from $$B$$. The ratio $$\displaystyle \left ( \frac{\lambda_A}{\lambda_B} \right )$$ of their wavelengths $$\lambda_A$$ and $$\lambda_B$$ at which the peaks occur in their respective radiation curves is
Heat Transfer
An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
Heat Transfer
A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays $$\log _{ 2 }{ \left( P/{ P }_{ 0 } \right)}$$ , where $${ P }_{ 0 }$$ is a constant. When the metal surface is at a temperature of $${ 487 }^{ \circ }C$$, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $${ 2767 }^{ \circ }C$$?
Heat Transfer
A human body has a surface area of approximately $$1 m^2$$. The normal body temperature is $$10 K$$ above the surrounding room temperature $$T_0$$. Take the room temperature to he $$T_0 = 300 K$$. For $$T_0 = 300 K$$ the value of $$\sigma T_0^4 = 460 Wm^{-2}$$ (where $$\sigma$$ is the Stefan-Boltzmann constant). Which of the following options is/are correct?
Heat Transfer
A black rectangular surface of area 'A' emits energy 'E' per second at 27$$^o$$C. If length and breadth are reduced to $$\dfrac{1}{3}rd$$ of initial value and temperature is raised to 327$$^o$$C then energy emitted per second becomes
Heat Transfer
The value of gravitational acceleration 'g' at a height 'h' above the earth's surface is $$\dfrac{g}{4}$$ then (R = radius of earth)
Heat Transfer
Two spheres of the same material have radii $$1m$$ and $$4m$$ and temperature $$4000K$$ and $$2000K$$ respectively. The energy radiated per second by the first sphere is :
Heat Transfer
Two spheres of the same material have radii $$1 m$$ and $$4 m$$ and temperatures $$4000 K$$ and $$2000 K$$ respectively. The ratio of energy radiated per second is
