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`.

Explanation

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