I need help on this problem. I keep getting -73 degrees Celsius,but this can\'t

Question

I need help on this problem. I keep getting -73 degrees Celsius,but this can't be right.


A 2-kg block of iron (c=0.11 kcal/ kg oC) that has beenbrought to a temperature of 500 oC is placed on top of a3 kg block of ice (c=0.5 kcal/kg oC) that has been cooledto -50 oC.   Assuming no heat is lost to thesurrounding container, what is the ?nal temperature of the ironblock?



Here's how I set up the problem, but I must be doing somethingwrong:

(heat to raise 3kg of ice from -50oC to 0oC) + (heat to change 3 kgof ice to water) + (heat to raise 3kg of water from 0oC to finaltemperature) = (heat lost by 2kg of iron cooling from 500oC tofinal temperature)

Therefore: mice cice (T) *miceLF * mwater cwater(T) = miron ciron (T)

[3kg * 0.5 kcal/kgoC * (50-0)] + [3kg * 79.7 kcal/kg] + [3kg *1kcal/kgoC * (T - 0)] = [2kg * 0.11 kcal/kgoC * (500-T)]

Explanation / Answer

The final temperature of the entire system will be zero deg C.This is because the iron will cool to zero, the ice will heat up tozero, and some of the ice will melt. It looks like you are assumingthat ALL of the ice will melt, but it does not. . How do I know? Experience... just looking at the numbers. Andyou know it also, because you assumed that all the ice melts andthen you got a goofy answer. Which means your assumption waswrong. . So the final system will be some iron, some ice and somewater, all at zero deg C. If you do not include the "ice melting"in your equation, it really goofs things up. Here is how it shouldlook: .       heat gained by ice to increasetemp to zero + heat to melt some ice = heat lost byiron when it is cooled to zero .       m c T      +    mL        =       m c T .      3 * 0.5 *50      +   m * 79.7  =    2 *0.11 * 500 .         75    +   m * 79.7   = 110 .               m * 79.7   =   35 .                  m =    0.439 kg . Notice this is the amount of ice that melted. It is areasonable answer because it is less than the amount of ice wehave! If the answer had come out greater than 3.0 kg, then itwould not have been reasonable. . Final state ofsystem:   2.0 kg iron, 0.439 kg water, 2.561kg ice   all at zero deg Celsius

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.