Heat and Thermodynamics 3 Question 19
19. 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
(a) 225
(b) 450
(c) 900
(d) 1800
$(1997,1 M)$
Show Answer
Solution:
- Power radiated $\propto$ (surface area) $(T)^{4}$. The radius is halved, hence, surface area will become $\frac{1}{4}$ times. Temperature is doubled, therefore, $T^{4}$ becomes 16 times.
New power $=(450)\left(\frac{1}{4}\right)(16)=1800 W$.
