Question 553: Thermodynamics & KTG

Question

Two spheres of the same material have radii $$1$$ $$m$$ and $$4$$ $$m$$ and temperatures $$4000$$ $$K$$ and $$2000$$ $$K$$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

Accepted Answer

The energy radiated per second is given by $$E = e\sigma {T^4}A$$
For same material $$e$$ is same. $$\sigma $$ is stefan's constant
$$	herefore$$ $${{{E_1}} \over {{E_2}}} = {{T_1^4{A_1}} \over {T_2^4{A_2}}} = {{T_1^44\pi r_1^2} \over {T_2^44\pi r_2^2}}$$
$$ = {{{{\left( {4000} ight)}^4} 	imes {1^2}} \over {{{\left( {2000} ight)}^4} 	imes {4^2}}} = {1 \over 1}$$

Answer

$$1:1$$

Answer

$$16:1$$

Answer

$$4:1$$

Answer

$$1:9$$

Thermodynamics & KTG

Two spheres of the same material have radii $1 m and 4 m and temperatures 4000 K and 2000 K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

Choose the correct answer: