Final Temperature of Water after Melting Ice: Solving for Unknown Variables

[knownothing1]

Homework Statement

A 100 g cube of ice at 0 degrees C is dropped into 1.0 g of water that was originally 80 degrees C. What is the final temperature of teh water after the ice has melted?

Homework Equations

What formula should be used in this problem? Am I forgetting variables?

The Attempt at a Solution

I used the following formula: MiceCpice(T2-T1)=MwaterCpwater(T2-T1)
(100g)(2108kJ/kg-k)(T2-0degreesC)=(1.0kg)(4184kJ/kg-k)(T2-80)
Any help will be greatly appreciated

 

[anathema]

!

your first step in responding to this forum post would be to check the formula used by the student. It is important to make sure that the correct units are used and that the equation is balanced. In this case, the student has correctly used the specific heat capacity (Cp) for ice and water, but has made a mistake in the units. The specific heat capacity should be in units of J/g-K, not kJ/kg-K. Additionally, there is a typo in the equation where "T2-80" should be "T1-80" to represent the change in temperature of the water.

The correct equation should be MiceCpice(T2-T1)=MwaterCpwater(T1-80).

After correcting the equation, you can solve for T2, the final temperature of the water. This will give you the final temperature in degrees Celsius. If you want the temperature in Kelvin, you will need to add 273 to the final temperature in degrees Celsius.

Another way to approach this problem is to use the heat gained by the water equals the heat lost by the ice.

Qwater = Qice

MwaterCpwater(T2-T1) = MiceCpice(T2-T1)

Solving for T2, you will get the same result as using the first equation.

It is also important to note that this equation assumes that the ice and water are in a closed system, meaning no heat is lost to the surroundings. In reality, some heat will be lost to the surroundings, so the actual final temperature may be slightly different.

 

[kerimek]

I would first confirm that the units used in the equation are correct. The specific heat capacity (Cp) of ice and water are typically given in units of J/g-K, so the units used in the equation should be J, not kJ. This may not affect the final answer, but it is important to use the correct units in scientific calculations.

Next, I would check to make sure that all the variables are accounted for and used correctly. In this case, the unknown variable is the final temperature of the water (T2). All other variables (mass, specific heat capacity, and initial temperature) are given and used correctly in the equation.

To solve for T2, you can rearrange the equation to isolate T2 on one side and solve for it. Alternatively, you can plug in the given values and solve for T2 using a calculator or spreadsheet.

Overall, your approach and formula used seem correct, but it is always important to double check units and variables to ensure an accurate solution.