Thermal Properties and Thermodynamics

Coefficient of absorption is defined as the ration of amount of radiation a body absorbs to the amount of radiation that is incident on the body.
Incident radiation = $p$
Rejected radiation = $q$
Hence absorbed radiation must be = $p - q$
From the definition of absorptive power it follows that the power = $\dfrac{p-q}{p}$

Coefficient of absorption is defined as the ration of amount of radiation a body absorbs to the amount of radiation that is incident on the body.
Incident radiation = $X$
Absorbed radiation  = $Y$
Hence absorptive power = $\dfrac{Y}{X}$

Given,

The net rate of heat loss by radiation is given by Stefan-Boltzmann law, P = e * sigma * A * (T1^4 - T2^4). Here, T1 = 127 degrees Celsius = 400 K, T2 = 27 degrees Celsius = 300 K, A = 6 * (1 m)^2 = 6 m^2, and emissivity e = 1/5.67. Substituting sigma = 5.67 x 10^-8 and the temperatures yields a heat loss rate of approximately 1.05 kW.

According to Kirchhoff law, good absorbers are good emitters. Since black spot is good absorbers so it is also a good emitter & will brighter than plate.

When a non black body is placed inside a hollow enclosure, the total radiation from the body is the sum of what it would emit in the open ( with $\epsilon<1$ ) and the part of the incident radiation from the walls reflected by it. The two add up to a black body radiation.

$P=\sigma e AT^4$

Calorific value is a measure of heating capacity of fuel. It gives the fuel efficiency.

The solar constant is the amount of solar energy reaching the upper atmosphere. The standard value is approximately 2 calories per square centimeter per minute.

$\begin{array}{l} { k _{ 1 } }\dfrac { { { T _{ 1 } }-{ T _{ c } } } }{ { { d _{ 1 } } } } ={ k _{ 2 } }\dfrac { { { T _{ c } }-{ T _{ 2 } } } }{ { { d _{ 2 } } } }  \ where\, { T _{ c } }\, is\, \, common\, \, wall\, temperature,\, solving\, for\, \, { T _{ c } }\, we\, \, will\, get \ { T _{ C } }=\dfrac { { { T _{ 1 } }+\alpha { T _{ 2 } } } }{ { \alpha +1 } }  \ u\sin  g\, \, \alpha =\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } \dfrac { { { k _{ 2 } } } }{ { { k _{ 1 } } } }  \ { T _{ c } }=\dfrac { { { T _{ 1 } }+\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } \dfrac { { { k _{ 2 } } } }{ { { k _{ 1 } } } } { T _{ 2 } } } }{ { \dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } \dfrac { { { k _{ 2 } } } }{ { { k _{ 1 } } } } +1 } }  \ =\dfrac { { { T _{ 1 } }\left( { { d _{ 2 } }{ k _{ 1 } } } \right) +{ T _{ 2 } }{ d _{ 1 } }{ k _{ 2 } } } }{ { { d _{ 1 } }{ k _{ 2 } }+{ d _{ 2 } }{ k _{ 1 } } } }  \ Hence,\, the\, option\, B\, is\, the\, \, correct\, answer. \end{array}$

For two slabs of equal thickness in series with thermal conductivities K1 = K and K2 = 2K, the equivalent thermal conductivity K_eq is given by the formula 2 / (1/K1 + 1/K2). Substituting the values yields 2 / (1/K + 1/(2K)) = 2 / (3/(2K)) = (4/3)K.

Conduction, convection and radiation are the mode of heat transfer whereas fusion is the nuclear reaction.

According to Newton's law of cooling, the rate of cooling depends on the surface area and emissivity. Since the spheres have the same material, size, and surroundings, they have the same surface area and emissivity, resulting in the same rate of cooling.

Since heat capacity increases with temperature, the body at 100 degrees Celsius has a larger heat capacity than the identical body at 0 degrees Celsius. When they reach thermal equilibrium, more heat is required to raise the temperature of the colder body per degree than the heat released by the hotter body, shifting the final common temperature higher than the simple arithmetic mean of 50 degrees Celsius.