Question

A baseball of radius r = 4.9 cm is at room temperature T = 19.4 C. The baseball has emissivity of ε = 0.81 and the Stefan-Boltzman constant is σ = 5.67 × 10-8 J/(s⋅m2⋅K4)

a - Say this ball is now moved to a region approximating T=0 K (space, for instance). Select an expression for the power radiated by the baseball, P1, right after it's moved from room temperature to 0 K.

b - What is the power in W?

Answer 1

Power radiated by baseball will be given by:

P = A*(Ti^4 - Tf^4)

A = Surface area of baseball = 4r^2

Ti = Initial temperature = T = 19.4 C = 292.4 K

Tf = final temperature = 0 K

So,

P = *(4r^2)*(T^4 - 0^4)

P = 4r²T⁴

Part B.

Using given values:

= emissivity of baseball = 0.81

= Boltzmann's constant = 5.67*10^-8

r = radius of bass = 4.9 cm = 0.049 m

T = 292.4 K

So,

P = 0.81*5.67*10^-8*(4*pi*0.049^2)*292.4^4

P = 10.13 W