Need help with mercury vs. water problem

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To determine whether it takes more energy to boil a gram of mercury or water, one must calculate the total energy required for both substances, including heating and vaporization. The specific heat of mercury is significantly lower than that of water, but its boiling point is much higher. The calculations involve using the formula Q = mc(Tf - Ti) for heating and adding the latent heat of vaporization for both substances. For water, the total energy includes raising its temperature to 100 degrees C and then vaporizing it, while for mercury, it involves heating to 357 degrees C and then vaporizing. Ultimately, the discussion emphasizes the importance of correctly applying these formulas to find the answer.
Aprilshowers
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I need help with a problem I have struggled with for several days.
Here is the problem:
The specific heat of mercury is .03 cal/g degrees C, and it's boiling point is
357 degrees C. The specific heat of water is 1 cal/g degrees C. It takes
65 calories of energy to vaporize one gram of mercury and 540 calories to
vaporize 1 gram of water. If both substances begin a room temperature
(about 22 degrees C), Does it take more energy to boil a gram of mercury or
a gram of water?
I found where the boiling point of water is 100 degrees C...but there is so
much information here that I cannot determine what is needed or not, and
what order to process the information...can anyone advise?
 
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You need to use Q = mc(T_{f} - T_{i})[/tex] for both the water and the mercury. T_{f}, T_{i} are the final and initial temperatures (which you are given for both water and mercury), c is the specific heat capacity and m is the mass (if you use J K^-1 kg^-1 and kg for those quantities, you'll get an answer in J).
 
Nylex said:
You need to use Q = mc(T_{f} - T_{i})[/tex] for both the water and the mercury. T_{f}, T_{i} are the final and initial temperatures (which you are given for both water and mercury), c is the specific heat capacity and m is the mass (if you use J K^-1 kg^-1 and kg for those quantities, you'll get an answer in J).
<br /> <br /> You also need the latent heat of vaporization given for each sustance. The question is asking the heat needed to raise the temperature of the liquid <b>and</b> to vaporize it.
 
Ahh ok, yeah.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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