Calculating initial temperature of iron block submerged into water

[ayans2495]

Homework Statement

A heated block of iron at temperature Ti with a mass of 61.331g is submerged into a beaker of water which has a mass of 200.562g and an inital temperature of 24.6 degrees Celsius. Once the iron is immersed into the water, 0.362 grams of the water evaporates. What is the initial temperature Ti of the iron block such that the final equilibrium temperature Tf is 34.3 degrees celsius?

Relevant Equations

Q=ml
Q=mcΔT Note: Δm=0.632

 

[ayans2495]

Is my solution correct? If not, may you please advise me on how to change it?

 

[ayans2495]

Also, Δm actually equals 0.362. I made an error there.

 

[haruspex]

Since your sign convention is unstated, it is hard to be sure whether your signs are correct. What numerical answer do you get?

(Quoting the masses to five and six figures when temperatures are only given to three is bizarre. Are you sure you have copied that correctly?)

 

[ayans2495]

I got that the initial temperature is 207 degrees Celsius as it was heated using a bunsen burner.

 

[haruspex]

I got that the initial temperature is 207 degrees Celsius as it was heated using a bunsen burner.

I get a considerably higher number. Please post the details of your working.

 

[ayans2495]

I get a considerably higher number. Please post the details of your working.

I simply inputted the values provided into the equation I derived and solved for TiI. The sign convention of Q3 I believe is negative as if I were to make it positive I would end up with a negative result.

 

[haruspex]

I simply inputted the values provided into the equation I derived and solved for TiI.

Yes, but I did the same and get a rather different number, so one of us has an error. Please post the equation with all the numbers filled in.

 

[ayans2495]

Yes, but I did the same and get a rather different number, so one of us has an error. Please post the equation with all the numbers filled in.

Perhaps I didn't round to the correct significant figures. When you asked whether or not I measured these correctly, the scale I used to measure these masses gave them in 4 to 5 s.f, but the thermometer in 3.May you please show me what values should be? I just posted my solution below.

 

[haruspex]

Perhaps I didn't round to the correct significant figures. When you asked whether or not I measured these correctly, the scale I used to measure these masses gave them in 4 to 5 s.f, but the thermometer in 3.May you please show me what values should be? I just posted my solution below.

Where does the 9.9866 figure come from? You gave the water mass as 200.562g.
Given the precision elsewhere, you should use 4186, not 4200.

 

[ayans2495]

Where does the 9.9866 figure come from? You gave the water mass as 200.562g.
Given the precision elsewhere, you should use 4186, not 4200.

Sorry the actual mass of the water is 99.866 grams. I will be sure to use 4186.

 

[haruspex]

Sorry the actual mass of the water is 99.866 grams. I will be sure to use 4186.

Ok, that gets us close enough together.
The other difference I see is that for the SH of iron you use 0.462. At https://www.engineersedge.com/materials/specific_heat_capacity_of_metals_13259.htm it gives 0.4605.

 

[ayans2495]

Ok, that gets us close enough together.
The other difference I see is that for the SH of iron you use 0.462. At https://www.engineersedge.com/materials/specific_heat_capacity_of_metals_13259.htm it gives 0.4605.

Great! Thank you so much for your help again!