a) At what depth in water is the pressure 37.6 times the pressure at the surface

Question

a) At what depth in water is the pressure 37.6 times the pressure at the surface, which is at 1 ATM ?

b) Two stars radiate as black bodies(e = 1). Star A has a radius three times as large as star B but a temperature 1/3 that of star B. If star B radiates a power of PB, what is the power PA radiated by star A?

c) Suppose the heat flow rate through a wall is H. If we double all the wall dimensions (height, width, thickness) but keep the temperature difference the same, what would the new heat flow rate be?

d) A hurricane wind blows horizontally across a 10m X 12m flat roof on a house. Find the wind speed that will produce an upward force of 2x10^5 Nt on the roof.

( 1ATM = 105 Pa, k = 1.38 x 10-23 J/degK)

Explanation / Answer

a)pressure at the surface   P _o = 1 ATM    presssure at depth P =   37.6 ATM            P = P_o + ? g h            ? g h = P - P _ o                  h = P - P _ o / ?g                      = ( 37.6 - 1 )*1.03*10^ 5 N / m^2 / (1000)(9.8)                      = 384.6 m b) power out put by star B is   P_B                       r_A = 3 r_B                                        intensity of star A is                         I = P_A / A = s T^4                               P_A = A_A s T^ 4                                   = ( 4p (3r_B)^2 ) (s )(T_B / 3 ) ^ 4                                   =   9 A_B  s( T_B)^4                                    = 0.11 P_B c)Heat flow rate Q = k A ?T / d              here A = area    If we double all the wall dimensions (height, width, thickness) but keep the temperature difference the same                 Q' = k ( 4A ) ?T / 2 d                    =   2 Q d)                                           

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