
#1
Feb2011, 05:14 PM

P: 13

1. The problem statement, all variables and given/known data
You want to heat 1 L of water by 10 ºC, and so you heat it with a mechanical egg beater that is powered by a 1 kg mass on a rope over a pulley. How far does the mass have to descend to supply enough work for heating the water? 2. Relevant equations work = mg(x_f  x_0) C_P (liquid water) = 75.3JK^1mol^1 3. The attempt at a solution I first asked myself how much energy does it take to increase the temp of 1kg of water by 10degC. Heat capacity of water (above) is the energy required to heat 1 mol of water by 1deg. So I first determined how many moles of water i have: 1L = 1kg = 1000g * (1mol/18.01g) = 55.5mol of liquid water Therefore 55.5mol *75.3JK^1mol^1 = 4179.15J/K * 10K = 417915.0J So it requires 417915.0J to raise the temp of 1kg water by 10degC. This is the work required also because work is also in joules, energy. Then i used the formula for mechanical work to determine the value for delta x. work = mg(x_f  x_0) 417915.0J(1kJ/10000J) = 1kg(9.81m/s/s)(x_f) (i got ride of x_0 because I set scale so that x_0 = 0) x_f = 42.6m So the mass has to descend through 42.6m in order to heat 1kg of liquid water by 10 degC. Is this correct or if not please help..thanks alot. I also have some other questions about the problem but i dont want to ask until i know if my answer is correct...thank you again 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


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