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A room heater is made of 10 polished thin walled tubes of copper, each one meter long are 5cm in diameter. If hot water at `70^(@)C` circulates constantly through the tubes, calculate the amount of heat radiated in an hour in a room where the average temperature is `15^(@)C` . Emissitivity of copper = `4 xx 10^(-2)cal//degree//sec//sq. metre`. |
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Answer» Here, no. of tubes , n=10 Length of each tube, `l=1 metre` Radius of each tube, `r = 5/2 cm = 5/200 m = 1/40 m` Surface area of each tube = `2 pi r l` and total area of all the tubes `A = 2 pi r l n` `= 2 xx 22/7 xx 1/40 xx 1 xx 10m^(2) = 11/7 m^(2)` Temperature of hot water `= 70^(@)C` Average room temperature = `15^(@)C` `:.` Difference of temperature, `theta = 70-15 = 55^(@)C` Emissivity, `epsilon = 4 xx 10^(-2) cals//sec//degree//sq.metre` Time, `t =1 hour = 3600 secs` Assuming that heat energy `radiated//sec//area` is directly proportional to temp. diff. `theta` the quantity of heat (Q) radiated = `A.theta . t epsilon` `:. Q = 11/7 xx 55 xx 3600 xx 4 xx 10^(-2)` `=1.245 xx 10^(4)` calories |
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