A stirrer rotates in 1l of water against a damping force of 0.1 N at 360 rpm in a circle of radius 5 cm. Calculate the rise in water temperature in 1 h, neglecting heat loss due to radiation . `(J k= 4.2 J cdot cal^(-1))`

Explanation

Mass of 1 l water, m = 1 kg
If t is the rise in temperature of water in 1h, then heat produced , H = mst
Now, circumference of the circle = `2 pi r` , number of rotations in 1 h = `360 xx 60`,
`:.` Displacement of the stirrer, `d = 360 xx 60 xx 2 pi r`,
Work done, `W = "force" xx "displacement"`
`= fd`
`:. W = JH or, Fd = J mst`
or, `t = (Fd)/(Jms) = (0.1 xx (360 xx 60 xx 2 xx pi xx 0.05))/(4.2 xx 1 xx 100)`
`[F = 0.1 N, r = 5 cm = 0.05 m`,
`s = 1000 cal cdot kg^(-1) cdot^(@)C^(-1)]`
`=0.162^(@)C`.