Using Figure 1 as a guide, calculate the length of time that the external electr

Question

Using Figure 1 as a guide, calculate the length of time that the external electrical cell will need to operate providing a potential difference of 1.5 V to equate the amount of change in the system that occurs when the weight falls 1 ft in the absence of the electric cell. Assume adiabaticity for both processes. The mass of the external weight is 45 lbs, the resistance of the electrical resistor is 2.0 k ohm, and the acceleration of free fall s 9.81 m/s^2. Electrical resistor and paddle wheel shown in water. Rectangle with dashed line represents the system boundary. The cross-hatched rectangle represents thermal insulation.

Explanation / Answer

As the process is adiabatic there is no loss of heat from the system.

now according to first law of thermodynamics energy is conserved

to equate energy of falling mass with electrical energy

electrical energy = E = (V2/R)t

V = potential difference

R = resistance

t = time

similarly E = mgh

m= mass

g = acceleration due to gravity

h= hight of weight fall

we will do all calculation in SI units for easy solution

1 lbs = 0.453592kg

45 lbs = 0.453592 *45 = 20.4117 kg

1 kOhm = 1000 ohm

1 foot = 0.3048 m

E(work) = E(electrical) given to solve

E(work) = mgh = 20.4117 kg * 9.81 m/s2 * 0.3048 m

= 61.032 Joule

61.032 Joule = (1.52 /1000)*t

61.032 *1000 / 2.25 = t

27125.33 s = t
7.53 hours = t

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