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588_Physics ProblemsTechnical Physics

588_Physics ProblemsTechnical Physics - 590 P20.47 Heat and...

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590 Heat and the First Law of Thermodynamics P20.47 P = = × × L N M O Q P σ π AeT 4 8 8 2 4 5 669 6 10 4 6 96 10 0 965 5 800 . . . W m K m K 2 4 e j e j a fb g P = × 3 77 10 26 . W P20.48 Suppose the pizza is 70 cm in diameter and A = 2 0 . cm thick, sizzling at 100°C. It cannot lose heat by conduction or convection. It radiates according to P = σ AeT 4 . Here, A is its surface area, A r r = + = + = 2 2 2 0 35 2 0 35 0 02 0 81 2 2 π π π π A . . . . m m m m 2 a f a fa f . Suppose it is dark in the infrared, with emissivity about 0.8. Then P = × = 5 67 10 0 81 0 80 373 710 10 8 4 3 . . . ~ W m K m K W W 2 4 2 e je j a fa f . If the density of the pizza is half that of water, its mass is m V r = = = = ρ ρπ π 2 2 500 0 35 0 02 4 A kg m m m kg 3 e j a f a f . . . Suppose its specific heat is c = ⋅° 0 6 . cal g C . The drop in temperature of the pizza is described by: Q mc T T dQ dt mc dT dt dT dt mc f i f f = = = = = ⋅° = ° d i b gb g P P 0 710 4 0 6 4 186 0 07 10 1 J s kg J kg C C s K s . . ~ P20.49 P = σ AeT 4 2 00 5 67 10 0 250 10 0 950 1 49 10 3 49 10 8 6 4 14 1 4 3 . . . . . . W W m K m K K 2 4 2 4 = × × = × = × e je j a f e j T T P20.50 We suppose the earth below is an insulator. The square meter must radiate in the infrared as much
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