Consider Joule\'s experiment described in the insight below. Assumethe mass m =

Question

Consider Joule's experiment described in the insight below. Assumethe mass m = 2.6 kg and thefluid is water with a volume of 0.82L. What is the increase in the temperature of the water when themass moves vertically a distance z = 0.67 m? THE EQUIVALENCE OF MECHANICAL ENERGYAND HEAT ENERGY In the 1840s, James Joule measured the mechanical equivalent of heat energy with an apparatus like the one shown in the figure . As a mass , falls through a height z, its potential energy is used to rotate a propeller in a liquid. The propeller's motion heats the liquid, increasing the liquid's temperature. According to the principle of conservation of energy, the change in potential energy of the mass is converted to heat energy. In this way, Joule was able to relate the unit used to at that time for heat energy (the calorie) to the unit of mechanical energy (the joule).

Explanation / Answer

Here Potential Energy is converted into heat energy and resultingin inmcrease in temperature change in Potential energy ,P = mgh = 2.6*9.8*0.67 = 17.0716 J Also, Volume of water = 0.82 L = 820 ml = 820 cc Density of water ,d = 1g/cc => mass of water, M = 820*1 g = 820g We know that, Heat , Q = MST where M = mass of water =820 g S = specific heat of water = 4.186 J/gK T = change in temperature As Potential Energy is converted into Heat energy => Q = P =>17.0716 = 820*4.186*T T = 4.973 *10-3 K Hence increase in temperature during this process is 4.973*10-3 K

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