Calculate the mass of ice with heat transfer / latent heat

In summary, the question involves finding the initial mass of ice, mi, given the initial and final conditions and the values for specific heat capacities and latent heat of fusion. The final temperature is 10C, indicating that the ice has melted completely. The equation Q=ml can be used to calculate the heat absorbed by the ice, which is equal to the heat released by the solid, Qs, since they are in thermal equilibrium. This can be used to solve for mi, which is 0.100kg.
  • #1
adam640
19
0

Homework Statement



Find mi, the initial mass of ice.

Ti = -20
ci = 2093Jkg-1K-1
Ts = +35
ms = 2kg
cs = 837.4Jkg-1K-1
cw = 4187Jkg-1K-1
lf = 3.35x105Jkg-1

S = solid
W = water
I = ice
lf = latent heat of fusion of ice / water

Homework Equations


Q=mc[tex]\Delta[/tex]T
Q=C[tex]\Delta[/tex]T
Q=ml

The Attempt at a Solution


For the Solid
Qs = (2)(837.4)(10-35)
Qs = -4.187x104J

For the Water / Ice
Qi = mix(4.186x104)
Q = mix(3.35x105)
Qw = mix(4.187x104)

I don't know where to go from here, I have seen the markscheme however and I am aware that the answer is: mi = 0.100kg
 
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  • #2
You've specified everything but the experimental circumstances. What are the initial and final conditions? Do you want to calculate the mass of ice remaining, or the initial mass of ice?
 
  • #3
Oops, the Solid is placed on top of the ice. The ice then melts and the final temperature of both the solid and the ice is 10. So basically I'm looking for the initial mass of the ice, before the rock was placed onto it.
 
  • #4
So, the final temperature is 10C. What does that tell you about the the water in the system?
 
  • #5


To calculate the mass of ice, we need to use the equations Q=mcΔT and Q=ml, where Q is the heat transferred, m is the mass, c is the specific heat capacity, ΔT is the change in temperature, and l is the latent heat of fusion.

First, we need to calculate the heat transferred during the solid-liquid phase change, which can be calculated using the formula Q=mlf. We know that the initial temperature of the ice is -20 degrees Celsius and the final temperature is 0 degrees Celsius, so the change in temperature is 20 degrees Celsius. Plugging in the values, we get:

Q = (2kg)(3.35x105Jkg-1) = 6.7x105J

Next, we need to calculate the heat transferred during the heating of the ice from 0 degrees Celsius to 35 degrees Celsius. This can be calculated using the formula Q=mcΔT. Plugging in the values, we get:

Q = (2kg)(2093Jkg-1K-1)(35-0) = 1.4x105J

Now, we need to calculate the heat transferred during the cooling of the water from 35 degrees Celsius to 0 degrees Celsius. This can also be calculated using the formula Q=mcΔT. Plugging in the values, we get:

Q = (2kg)(4187Jkg-1K-1)(35-0) = 2.3x105J

Finally, we can calculate the total heat transferred by adding the values from the three steps:

Qtotal = 6.7x105J + 1.4x105J + 2.3x105J = 1.0x106J

Now, we can use the formula Q=mcΔT to find the mass of ice (mi) using the heat transferred (Qtotal) and the specific heat capacity of ice (ci). Rearranging the formula, we get:

mi = Qtotal / (ciΔT) = (1.0x106J) / ((2093Jkg-1K-1)(20K)) = 0.100kg

Therefore, the initial mass of ice is 0.100kg.
 

What is the formula for calculating the mass of ice with heat transfer and latent heat?

The formula for calculating the mass of ice with heat transfer and latent heat is: m = Q / L, where m is the mass of ice, Q is the amount of heat transferred, and L is the latent heat of fusion for ice.

How do you determine the amount of heat transferred in a system involving ice?

The amount of heat transferred in a system involving ice can be determined by taking the difference between the initial and final temperatures of the system and multiplying it by the specific heat capacity of ice (c) and the mass of the ice (m). This can be represented by the equation Q = m x c x ΔT.

What is the latent heat of fusion for ice?

The latent heat of fusion for ice is the amount of energy required to change one unit of mass of ice into liquid water at its melting point without changing its temperature. It is equal to 334 joules per gram.

Can the mass of ice be calculated if the amount of heat transferred is unknown?

No, the mass of ice cannot be calculated if the amount of heat transferred is unknown. The equation m = Q / L requires the value for Q to be known in order to calculate the mass of ice.

What units should be used for the calculation of the mass of ice with heat transfer and latent heat?

The units used for the calculation of the mass of ice with heat transfer and latent heat should be consistent. The mass should be in grams, the heat should be in joules, and the latent heat should be in joules per gram.

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