Change in Temperature and Thermal Energy?

[seichan]

[SOLVED] Change in Temperature and Thermal Energy?

Question- A physicist, upon awaking one morning to find his stove out of order, decides to boil the water for his wife's coffee by shaking it in a thermos flask. Suppose that he uses 420 cm^3 of tap water at 55 degF, that the water falls 1.45 ft each shake, and that the physicist completes 26 shakes each minute. Neglecting any loss of thermal energy by the flask, how long must he shake the flask before the water boils?

Work-Alright, so we know that Q=m*c*(Tf-Ti). We know the density of the water and can easily obtain the mass from there (420 g). Cwater is equal to 4.186 J/(g*K). We can convert Fahrenheit to Kelvin (55 degF is 285.77777 degK). This is Ti and Tf is 373 K.
Q=420(4.186)(373-285.777)
Q=153383.764517
Now, calculate the work done by the shaken thermos. F*d (m*a*d). The mass is 420, the acceleration is (1.45 ft*26)/min*1/60 or .6283333. Set this equal to heat, with distance as a variable.
420*.6288*x=153383.764
x=580.7066 ft
Multiply by number of ft/s...
=364.87733 s

Does anyone know where I'm going wrong? Thank you so much in advance for any help you may give me.

 

[jbsteele]

Answer: You were going wrong in your calculation of the work done by the shaken thermos. The force exerted on the thermos is not equal to the mass times the acceleration (F = ma). The force is actually equal to the mass times the acceleration due to gravity, which would be 9.81 m/s^2 or 32.174 ft/s^2. So the equation for work should be W = F*d = (m*g*d) = (420 g * 32.174 ft/s^2 * 580.7066 ft). This gives a total work of 8,894.35 J.Now, we can solve for the time required to complete this work by dividing the total work by the power output of the physicist (which is calculated as P = W/t). The power output of the physicist is 8,894.35 J/min or 148.239 J/s. Therefore, t = W/P = 8,894.35 J/148.239 J/s = 60.0 seconds. So the answer is 60 seconds.

 

[Moetasim]

Response- It seems like you are on the right track with your calculations and understanding of the relationship between thermal energy and temperature change. However, it is important to note that the work done by shaking the thermos is not the same as the heat absorbed by the water. The work done is the force applied multiplied by the distance moved, while the heat absorbed is the mass of the water multiplied by the specific heat capacity and the change in temperature. Therefore, the equation should be F*d = m*c*(Tf-Ti). Also, the units for the force and distance should be in the same system (either both in metric or both in imperial units). Additionally, you may want to double check your conversion from feet to meters, as it appears to be slightly off. Overall, your approach is correct, but there may be some minor errors in your calculations. Keep up the good work!