2 The figure below depicts the experiment Joule used to show

2. The figure below depicts the experiment Joule used to show the equivalency echanical work. Equal masses were placed of heat and mechanical work. Nual masses were placed on each pan, which created a force that is labeled “W” in the diagram. (Even Joule had trouble keeping mass and weight straight.) During the experiment, the mass was allowed to drop a known distance. The masses were connected to paddles via a wire and pulley system. The paddles stirred a sample of water. Joule would then measure the temperature rise in the water. Joule insulated the water beaker, but initially assumed that the heat absorbed by the paddles was negligible.

Solution

a. Work done = 2*(mg)*h = 2*50*5 = 500 lbf-ft

Temperature rise of water dT= 60.5 - 60 = 0.5 ^oF or ^oR

If C is the specific heat of water, then, heat stored in water = m_w*C*dT = 1.22*C*0.5 = 0.61C

So, according to the first law of thermodynamics, 0.61C = 500, so C = 819.67 lbf-ft/lbm-R

(b) Assumptions: There is no other source of heat loss, the entire energy is converted into heat. The heat loss to the paddle is negligible. Insulation is perfect insulation.

(c) % error in heat capacity = ((778-819.67)/778)*100% = -5.53%

So, the heat capacity calculated by Joule was 5.53% higher than the actual value.

(e) In the initial experiment, the temperature measured was not accurate. So when he make the temperature change as constant, that elimintaed any error caused by the measurement of temperature. And thus a better accuracy is obtained.