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A human body has a surface area of approximately 1 m^(2) . The normal body temperature is 10 K above the surrounding temperature T_(0). Take the room temperature to be T_(0)=300 K. For T_(0)=300 K, the value of sigma T_(0)^(4) =460 Wm^(-2) (wher sigma is Stefan-Boltzmann constant). What of the following option is/are correct ? |
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Answer» The amount of energy radiated by the body in/SECOND is close to 60 joules. (a) `E=sigma A(T^(4)-T_(0)^(4)) =sigma (T^(4)-T_(0)^(4))``(.: A= 1m^(2))` `=sigma[(T_(0) + 10)^(4) - T_(0)^(4))] =sigma T_(0)^(4)[(1+(10)/(T_(0)))^(4) - 1]` `=sigma T_(0)^(4)[1 +(4xx10)/(T_(0)) + ... -1] ~~ sigma T_(0)^(4) xx(40)/(T_(0))` `460xx(40)/(300)=61.33 ~~ 60` joule Energy radiated in 1 second `~~ 60` joule [Thus option (a) is true ]. (b) When surrounding temperature reduces by a small amount `Delta T_(0)` , keeping the body temperature T constant, the amount of HEAT energy radiated per second per unit are is `E =sigma[T^(4) - T_(0)^(4)]` `dE =sigma[0 - 4T_(0)^(3) Delta T_(0)]``[But Delta T_(0) =-Delta T_(0)]` So `dE =sigma 4T_(0)^(3) Delta T`[Thus option (b) is true] (c) Since energy radiated per second from a body is directly proportional to the surface area of the body. By curbing, the surface area decreases, so energy radiation decreases. Thus option (c) is true. (d) When the body temperature rises, the peak in the spectorum of electromagnetic radiation emitted by the body shifts towards lower, wavelength side (ac cording to Wien's law). Thus option (d) is wrong. |
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