Help confusion on heat transfer.

In summary, the problem involves calculating the amount of ice (in grams) at 0 degrees Celsius needed to cool 250g of water at 40 degrees Celsius to 35 degrees Celsius. The equation used is the summation of heat, where the sensible heat of melted ice, latent heat of ice, and sensible heat of water at 40 degrees Celsius are considered. The correct answer given by the professor is 16.73kg, while the student's solution resulted in 10.89kg, which may be due to incorrect unit conversions. Further review and correction may be needed.
  • #1
macmac410
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0

Homework Statement


Calculate the amount (in grams) of ice at 0 degree celsius that must be added to an insulated cup with 250g of water at 40 degree celsius to cool the water to 35 degree celsius. ignore heat transfer to the cup.

given data:
T(initial) water= 40 celsius
T(initial) ice = 0
T(final for both h20 and melted ice) = 35

latent heat of fusion of h20 = 334x10^3 j/kg
Heat capacity of h20 = 4190 j/kgC

Homework Equations



Summation of heat = Heat ice + heat h20 (breaking down heat of ice = latent heat of ice + sensible heat of ice)

Summation of heat = sensible heat of melted ice + latent heat of ice + sensible heat of h2o at 40)

Qsensible=m(Heat capacity)(deltaT)
Qlatent=m(latent heat of Fusion)

The Attempt at a Solution



this is my solution on the problem but as my professor check it, it was wrong, the correct answer that my professor given is 16.73kg, i doubted it because i did a lot of research and thinking in this. and I am shy to correct my professor if his given answer is wrong. please help me if my answer is the right one or is it my professor answers. i have an exam tomorrow and i can't seem to get the right answers unless if my answers is true please correct me if i have miscalculate something or overlooked somthing at my given solution and answers. Thanks you very much. please help me

the sum of heat is equal to zero since we will ignore the transfer of heat to its environment we will just consider the transfer from h2o to ice.

Summation of heat = sensible heat of melted ice + latent heat of ice + sensible heat of h2o at 40)0=m(Heat capacity)(deltaT)melted ice+m(latent heat of Fusion) ice + m(Heat capacity)(deltaT)h2o

transpose Q of h2o

-[m(Heat capacity)(deltaT)h2o]= m(Heat capacity)(deltaT)melted ice + m(latent heat of Fusion) icefactor out mass that is the same on ice

-[m (Heat capacity)(deltaT)h2o]= m [(Heat capacity)(deltaT)melted ice + (latent heat of Fusion) ice]equate to get the mass

m =-[m(Heat capacity)(deltaT)h2o] / [(Heat capacity)(deltaT)melted ice + (latent heat of Fusion) ice]substitute the givenm= - [(0.25)(4190)(35-40)]/ [(4190)(35-0)+(334x10^3)]

m=0.01089 grams x 1000 = 10.89kg
 
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  • #2
According to your calculations (and your professor's), if I want to cool a glass of water a few degrees, I should use a block of ice about 40 times the mass of the glass of water. I think you and your professor need to put on your thinking caps and recheck your units.

(Ahh, the simplicity of the metric system.)
 

1. What is heat transfer?

Heat transfer is the movement of thermal energy from one object or substance to another. This can occur through three main mechanisms: conduction, convection, and radiation.

2. Why is understanding heat transfer important?

Understanding heat transfer is important because it plays a crucial role in many scientific and technological processes, such as cooking, heating and cooling systems, and material processing. It also helps us understand and predict the behavior of various natural phenomena, such as weather patterns and climate change.

3. How does heat transfer work?

Heat transfer works by transferring thermal energy from a high temperature region to a low temperature region. This can occur through direct contact between objects (conduction), the movement of fluids or gases (convection), or the emission and absorption of electromagnetic radiation (radiation).

4. What factors affect heat transfer?

The rate of heat transfer is affected by several factors, including the temperature difference between the two objects, the thermal conductivity of the materials involved, the surface area and distance between the objects, and the presence of any insulating materials.

5. How can heat transfer be calculated or measured?

Heat transfer can be calculated or measured using various equations and methods, depending on the specific situation. For example, for conduction, the rate of heat transfer can be calculated using Fourier's Law, while for convection, it can be measured using a heat flux sensor. Radiation can also be calculated using the Stefan-Boltzmann Law.

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