Question

James Joule used a spinning set of paddles to heat the water in which they were placed, and by comparing the mechanical energy he put in, and temperature rise of the liquid afterwards, he determined the interconversion between mechanical and thermal energy.    Inspired by Joule's experiment, you decide to heat your bath water by pushing your hand through it in circles. Estimate the total distance your hand will have travelled to raise the water temperature by 10°C in a typical bathtub. You may assume your hand exerts a continuous force of 50 N.

Answer 1

Apply the energy conservation -

Work done by force = thermal energy transferred to water

Work done by force = force x distance

= 50x. ( x = distance )

50 x =. mC_{​​​​​P}​ T.  

T = temperature rise

Let's take m = 1 kg

C_{​​​​​​P} = 4180 J /Kg - K for water

x. =. 4180 x 1 x 10 / 50

=. 836 metres .

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