How Many Grams of Ice Will Melt When Iron Meets Ice?

[Kaleb]

[SOLVED] Thermo Energy. Iron + Ice

Homework Statement

A 50-g chunk of 80 degree C iron is dropped into a cavity in a very large block of ice at 0 degrees C. How many grams of ice will melt? (The specific heat capacity of iron is .11 cal/g*C)

Homework Equations

Q = cmdeltaT
Quantity of heat = heat capacity * mass * change in temp

also i know that it takes 80 calories to go just from ice to water

The Attempt at a Solution

All my attempts have met with failure:

1) .11cal/g*C * 50g(x-80C)=.5*y(x-0C) (i don't know the mass of ice so I am clueless on how to solve this)

2) .11cal/g*c *50g(0-80C)=.5*y(0-0C) (assuming that the ice will equalize the final temp but it leaves the right equation = 0 which makes it pointless.

There is a re-occurring number that I keep having and its 440 cal/g. Any and all help is appreciated.

I figured it out, my second equation was correct. Thanks though!

 

[lippyka]

Q=mc∆T.11cal/g*C *50g(0-80C) = 440cal440cal/80C = .11cal/g*C *50g440cal/50g = .88cal/g*C = mm = 440cal/50g/.88cal/g*Cm = 500g

 

[Moetasim]

I would approach this problem by first identifying the known values and the unknown value. The known values are the mass of the iron (50 g), its initial temperature (80 degrees C), the specific heat capacity of iron (0.11 cal/g*C), and the final temperature after the iron is dropped into the ice (0 degrees C). The unknown value is the mass of ice that will melt.

Using the formula Q = cmdeltaT, we can calculate the quantity of heat that is transferred from the iron to the ice. The change in temperature (deltaT) for the iron is 80 degrees C (since it goes from 80 degrees C to 0 degrees C), and for the ice, it is 0 degrees C (since it goes from 0 degrees C to 0 degrees C).

Thus, we have Q = (0.11 cal/g*C)(50 g)(80 C) = 440 cal.

We also know that it takes 80 calories to melt 1 gram of ice. Therefore, the mass of ice that will melt can be calculated as:

440 cal = (80 cal/g)(x g)

Solving for x, we get x = 5.5 g. Therefore, 5.5 grams of ice will melt when the 50 g chunk of iron at 80 degrees C is dropped into the cavity in the ice at 0 degrees C.

I hope this explanation helps. Please let me know if you have any further questions.