Find the mass and side length of unknown ice cube?

AI Thread Summary
To find the mass and side length of an unknown ice cube that absorbs 650 EJ of energy while heating from -10°C to 20°C, the problem can be broken into three parts: heating the ice to 0°C, phase change from ice to water, and heating the water to 20°C. The specific heat of ice and water, along with the heat of fusion, are crucial for calculations using the equations q=mc(t2-t1) and q=m(F). It's important to note that the total energy of 650 EJ is not divided among the three phases but is the cumulative energy for the entire process. By calculating the energy required for 1 kg of ice to transition from -10°C to 20°C, the mass of the ice cube can be determined in relation to the total energy input. The discussion highlights the massive scale of energy involved, comparing it to the total energy consumption of the United States over several years.
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Homework Statement


transfer 650 EJ (10^18 joules) into an ice cube of unknown size. the temperature of h20 increases from -10c to 20c.

Given:
1) q=mc(t2-t1)
2) for phase change q=m(F)

specific heat of ice (c)= 2.22x10^3 J.kg^-1.K-1
heat of fusion (f)= 3.33x10^5 J/kg
specific heat of water (c) = 4186 J.kg^-1.K^-1)

Homework Equations


what is the side length and mass of cube?

The Attempt at a Solution


First I would use eqn 1 for the heating of ice from (-10C to 0C): q=650EJ, c t= 10C and solve for mass?
then use second equation for phase change solid to liquid (0C) using q=650,f and also solve for mass?
use eqn 1 again and solve for m of water going from (0C to 20C) q=650EJ, c, t=20c

Then I would sum the masses and solve for volume?
 
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It's good that you see to break the problem up into 3 parts. However, in your solution you have assumed that 650 EJ are added for each part. But, 650 EJ is the total amount of heat added for the entire process of going from -10 C to 20 C.
 
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I am not given any mass information so I cannot find Q of each step. any way to combine the equations? like Q= (m)(c)(t) + (m)(f)
 
How much heat does it take to start out with 1 kg of ice at -10 C and end up with liquid water at 20 C?
 
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Thank you for the responses, I appreciate it! so I figure out how much energy it takes for 1kg of ice to go from -10c to 20c and then I can use that relationship to figure out mass with 650EJ?
 
Adam_9333 said:
Thank you for the responses, I appreciate it! so I figure out how much energy it takes for 1kg of ice to go from -10c to 20c and then I can use that relationship to figure out mass with 650EJ?
Sure
 
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