Thermal Radiation: Black Body, Stefan & Wien

If $150$ J of energy is incident on area $2\text{ m}^2$ and amount of heat reflected is $15$ J, coefficient of absorption is $0.6$ the amount of energy transmitted is

Heat energy is incident on the surface at the rate of $1000$ J/min. If coefficient of absorption is $0.8$ and coefficient of reflection is $0.1$ then heat energy transmitted by the surface in 5 minute is

When $170$ J of energy is incident on a surface of a body, $17$ J of energy is reflected by it. If the coefficient of absorption is $0.7$, then the amount of energy transmitted will be

'$x$' joule of heat is incident on a body. Out of it, the total heat reflected and transmitted by it is '$y$' joule. The absorption coefficient of the body is

A perfectly black body radiates power at temperature $T_1$ K. If it is to radiate 16 times this power, its temperature should be increased by

The temperature of a black body is increased by $50\%$ then the percentage increase of radiation is nearly

A black body is at temperature $827^\circ$C. The rate at which it emits energy is proportional to

Temperature of two stars are in the ratio $3 : 2$. If wavelength of maximum intensity of first star is $4200$ Å, the corresponding wavelength for second star is

Identify the INCORRECT statement about the black body radiation

Two stars A and B radiate maximum energy at wavelength $3.9 \times 10^{-7}$ m and $5.2 \times 10^{-7}$ m respectively. The ratio of the temperature of star A to that of star B will be

Out of the following, which statement is NOT true about black body radiation?

A black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature 'T' K. Its corresponding wavelength at temperature $(2.5T)$ K will be

About black body radiation, which one of the following is a WRONG statement?

Two bodies 'X' and 'Y' at temperatures $T_1$ K and $T_2$ K respectively have the same dimensions. Their emissivities $e_1$ and $e_2$ are in the ratio of $1 : 6$. If their emissive powers are same, the relation between their temperatures is

Rate of radiation by a black body is 'R' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is

A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

At $273^\circ$C, the emissive power of a perfectly black body is $R$. The value at $0^\circ$C is

The radiation emitted by a star A is $10000$ times that of the sun. If surface temperature of sun and star A are $6000$ K and $2000$ K respectively, the ratio of radii of star A and sun is

The total radiant energy per unit area normal to the direction of incidence, received at a distance R from the centre of a star of radius r, whose outer surface radiates as a black body at a temperature 'T' K is ($\sigma$ = Stefan's constant)

A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at 400 K is $\frac{x}{243}$. The value of $x$ is (Temperature of surrounding is 300 K)

A sphere is at temperature $600$ K. In an external environment of $200$ K, its cooling rate is R. When the temperature of the sphere falls to $400$ K then cooling rate R' will become

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperature $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be

In an external environment of temperature ($T$) kelvin, a sphere at temperature ($3T$) kelvin has cooling rate $R_1$. When the temperature of that sphere falls to ($2T$) kelvin, the cooling rate $R_2$ of the sphere will become

What will be the ratio of rate of radiation of metal sphere at two different temperatures $T_1 = 527^\circ$C and $T_2 = 127^\circ$C

The wavelength of maximum intensity of radiation emitted by a star is $289.8$ nm. The radiation intensity of the star is (Stefan's constant = $5.67 \times 10^{-8}$ SI unit, Wein's constant $2898\,\mu$mk)

A rectangular black body of temperature $27^\circ\text{C}$ has surface area $6$ cm $\times 3$ cm and rate of radiation $E$. If its temperature is increased by $300^\circ\text{C}$ and its linear dimensions are reduced to $\left(\frac{1}{3}\right)^{rd}$ of their initial value then the rate of radiation is

A black body is at temperature of 5780 K. The energy of radiation emitted by the body at wavelength 300 nm is $U_1$, at wavelength 500 nm is $U_2$ and that at 900 nm is $U_3$ respectively. Wien's constant $b = 2.89 \times 10^{6}$ nmK. This shows that

A black rectangular surface of area 'A' emits energy 'E' per second at $27^\circ$ C. If length and breadth is reduced to half of its initial value and temperature is raised to $327^\circ$C then energy emitted per second becomes

A black rectangular surface of area A emits energy E per second at $127^\circ$ C. If length and breadth is reduced to half of initial value and temperature is raised to $527^\circ$ C then energy emitted becomes

A black rectangular surface of area A emits energy E per unit time at $27^\circ$ C. If length and breadth is reduced to $\left(\frac{1}{4}\right)^{th}$ of initial value and temperature is raised to $327^\circ$ C, then energy emitted per unit time becomes

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $0.75\lambda_0$, the power radiated by it becomes $nP$. The value $n$ is

The power radiated by a black body is P and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3\lambda_0}{4}$, the power radiated by it becomes nP. The value of n is

A black body radiates maximum energy at wavelength '$\lambda$' at temperature $T_1$ and its emissive power is E. When the temperature of the body is changed to $T_2$, it radiates maximum energy at wavelength $\frac{2\lambda}{3}$, then the emissive power will become

The energy spectrum of a black body exhibits a maximum around a wavelength '$\lambda$'. The temperature of the black body is now changed such that the energy is maximum around a wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda$. The temperature of a black body is now changed such that the energy is maximum at wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor of

A black disc has a radius 'R' and wavelength corresponding to the maximum intensity is '$\lambda$'. The emissive power (E) for the different radii and maximum wavelengths is directly proportional to

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\frac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

Three spheres, P, Q and R, having radii $4$ m, $5$ m and $6$ m respectively, are coated with lamp black on their outer surfaces. The wavelengths corresponding to maximum intensity (radiated) are $400$ nm, $500$ nm and $600$ nm respectively. If the powers radiated by them are $P_P, P_Q$ and $P_R$ respectively, then $P_P : P_Q : P_R$ is

If 120 J of thermal energy is incident on area $3\text{ m}^{2}$, the amount of heat transmitted is 12 J, coefficient of absorption is 0.6, then the amount of heat reflected is

For a perfectly black body, coefficient of emission is

The co-efficient of absorption and the coefficient of reflection of a thin uniform plate are 0.77 and 0.17 respectively. If 250 kcal of heat is incident on the surface of the plate, the quantity of heat transmitted is

Black sphere of radius R radiates power P at certain temperature $T$. If the temperature is doubled, the radius gets doubled. Now the power radiated would be

A black body has maximum wavelength ' $\lambda_{m}$ ' at temperature 2000 K. Its maximum wavelength at 3000 K will be

A black body emits radiation of maximum intensity at wavelength ' $\lambda$ ' at temperature T K. Its corresponding wavelength at temperature 1.5 T K will be

The following graph represents the radiant power versus wavelength of the black body. The area under the curve represents

Two bodies A and B at temperatures ' $T_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. Their emissivities are in the ratio $16 : 1$. At $T_1 = xT_2$, they radiate the same amount of heat per unit area per unit time. The value of $x$ is

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^\circ\text{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x =$ _________. (Given $\sigma = 6.0 \times 10^{-8}\text{ W m}^{-2}\text{ K}^{-4}, \pi = 3.14$ and assume that the emissivity of wire material is same at all wavelength.)

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' $R$ ' from the centre of a star of radius ' $r$ ' is $(R > r)(\sigma =$ Stefan's constant $)$

Two spherical black bodies have radii ' $R_1$ ' and ' $R_2$ '. Their surface temperatures are ' $T_1$ ' and ' $T_2$ '. If they radiate same power, then $\frac{R_2}{R_1}$ is

A black sphere has radius $R$ whose rate of radiation is E at temperature T. If radius is made R / 2 and temperature 3T, the rate of radiation will be

Two spherical black bodies have radii ' $R_1$ ' and ' $R_2$ '. Their surface temperatures are $T_1 K$ and $T_2 K$ respectively. If they radiate the same power, the ratio $\frac{R_1}{R_2}$ is

If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' $R_0$ ', the same body at 900 K, surrounded by same atmosphere, will have rate of cooling nearly

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K. If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

A rectangular black body of temperature $127^\circ\text{C}$ has surface area $4\text{ cm} \times 2\text{ cm}$ and rate of radiation is E. If its temperature is increased by $400^\circ\text{C}$ and surface area is reduced to half of the initial value then the rate of radiation is

Black bodies A and B radiate maximum energy with wavelength difference $4\,\mu\text{m}$. The absolute temperature of body A is 3 times that of B. The wavelength at which body $B$ radiates maximum energy is

A rectangular block of surface area A emits energy E per second at $27^\circ\text{C}$. If length and breadth is reduced to half of initial value and temperature is raised to $327^\circ\text{C}$ then energy emitted per second becomes

Two black spheres $P \,\&\, Q$ have radii in the ratio $4 : 3$. The wavelength of maximum intensity of radiation are in the ratio $4 : 5$ respectively. The ratio of radiated power by P to Q is

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' joule. The absorption coefficient of body is

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio $T_1 : T_2$ is

Rate of radiation by a black body is ' R ' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is

A black sphere has radius $R$ whose rate of radiation is E at temperature T. If radius is made half and temperature 4 T, the rate of radiation will be

Two bodies ' X ' and ' Y ' at temperatures ' $T_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is

A sphere is at temperature 600 K. In an external environment of 200 K, its cooling rate is ' $R$ ' When the temperature of the sphere falls to 400 K, then cooling rate ' $R'$ ' will become

Two spherical black bodies of radii ' $R_1$ ' and ' $R_2$ ' and with surface temperature ' $T_1$ ' and ' $T_2$ ' respectively radiate the same power. The ratio of ' $R_1$ ' to ' $R_2$ ' will be

Ordinary bodies P and Q radiate maximum energy with wavelength difference $3\,\mu\text{m}$. The absolute temperature of body P is four times that of Q. The wavelength at which body Q radiates maximum energy is

The frequency ' $\nu_{\text{m}}$ ' corresponding to which the energy emitted by a black body is maximum may vary with the temperature ' $T$ ' of the body as shown by the curves ' A ', ' B ', ' C ' and ' D ' in the figure. Which one of these represents the correct variation?

The power radiated by a black body is P and it radiates maximum energy around the wavelength $\lambda_0$. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength $\left(\frac{\lambda_0}{2}\right)$. The power radiated by it will now increase by a factor of

The black discs $x, y$ and z have radii $1\text{ m}, 2\text{ m}$ and 3 m respectively. The wavelengths corresponding to maximum intensity are $200\text{ nm}, 300\text{ nm}$ and 400 nm respectively. The relation between emissive power $E_x, E_y$ and $E_z$ is

A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength $\frac{\lambda_0}{4}$. The power radiated by it at new temperature is

A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission respectively)

Heat energy is incident on the surface at the rate of X J/min. If '$a$' and '$r$' represent coefficient of absorption and reflection respectively then the heat energy transmitted by the surface in '$t$' minutes is

If the temperature of a hot body is increased by $50\%$, then the increase in the quantity of emitted heat radiation will be approximately

About black body radiation, which of the following is the wrong statement?

Two bodies $A$ and $B$ at temperatures '$T_1$' $\text{K}$ and '$T_2$' $\text{K}$ respectively have the same dimensions. Their emissivities are in the ratio $1 : 3$. If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures $(T_1 : T_2)$ is

A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and in same atmosphere. The ratio of their rate of loss of heat will be

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $200^\circ\text{C}$. When these are left in a room.

A black body at temperature $127^\circ\text{C}$ radiates heat at the rate of $5\text{ cal/cm}^{2}\text{ s}$. At a temperature $927^\circ\text{C}$, its rate of emission in units of $\text{cal/cm}^{2}\text{ s}$ will be

Compare the rate of loss of heat from a metal sphere at $627^\circ\text{C}$ with the rate of loss of heat from the same sphere at $327^\circ\text{C}$, if the temperature of the surrounding is $27^\circ\text{C}$. (nearly)

A black sphere has radius '$R$' whose rate of radiation is '$E$' at temperature '$T$'. If radius is made $R/3$ and temperature '$3T$', the rate of radiation will be

Two spherical black bodies of radii '$r_1$' and '$r_2$ ' at temperature '$T_1$ ' and '$T_2$' respectively radiate power in the ratio $1 : 2$ Then $r_1 : r_2$ is

A black body radiates maximum energy at wavelength '$\lambda$' and its emissive power is '$E$'. Now due to a change in temperature of that body, it radiates maximum energy at wavelength $\frac{\lambda}{3}$. At that temperature emissive power is

A black body radiates maximum energy at wavelength '$\lambda$' and its emissive power is 'E' Now due to change in temperature of that body, it radiates maximum energy at wavelength $\frac{2\lambda}{3}$. At that temperature emissive power is

A black body radiates maximum energy at wavelength '$\lambda$' and its emissive power is $E$. Now due to change in temperature of that body, it radiates maximum energy at wavelength $\frac{2\lambda}{3}$. At that temperature emissive power is

Three discs $x, y$ and $z$ having radii $2\text{ m}, 3\text{ m}$ and $6\text{ m}$ respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are $300\text{ nm}, 400\text{ nm}$ and $500\text{ nm}$ respectively. If $P_x, P_y$ and $P_z$ are power radiated by them respectively then