If we have 2 black bodies (1 & 2). The temperature of (1) is 1000K and that of (

Question

If we have 2 black bodies (1 & 2). The temperature of (1) is 1000K and that of (2) is 3000K. In which circumstance can (1) radiate more total power than (2)? Is this true when (1) has more surface area than (2)?

Explanation / Answer

P/A = s T^4 where s is the Stefan–Boltzmann constant, s ˜ 5.67 × 10-8 W/(m2K4). Power P radiated over the given area A a temperature T. P is directly proportional to T^4 and directly proportional to Area A now given that T1=1000K and T2=3000K. P1/P2 = (T1/T2)^4 * (A1/A2) P1/P2 = (1000/3000)^4 * (A1/A2) P1/P2= 1/81 * A1/A2 So P1 > P2 only when A1/A2 > 81 or in words area of body 1 should be more than 81 times the area of body 2. In that circumstance only body 1 radiates more total power than body 2 . Hence its true only when body 1 has more surface area than body 2 and that too only when its more than 81 times the area of body 2

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