[lakp]

hi! what is the specific heat capacity (heat fusion) of ice?

this is just one part of a greater problem I would really appreciate an explanation for ..
here goes ...

water and ice co-exist (or something like that ...) at 0 degrees celsius.  So, i have water and ice at 0 degrees celsius in a calorimeter, and the ice weighs 50 grams.  I know that when a 35 gram metal ball, at 100 degrees celsius with a specific heat capacity of .442J/gXdegrees celsius is placed in this ice/water solution, the heat released from the metal ball will only go into the ice to heat the ice (heat does not effect the water, it just goes to the ice and melts the ice ..).  So, in the end, we have our ice that was first 50 grams, now melted to 48 grams.  And the metal ball has gone from 100 degrees to 0 degrees.

How can I measure the specific heat capacity of this ice.  I know that the ball released 1547 juoles of energy (q=m X C X change in temp).  But, im stuck on calculating the heat capacity needed to raise 1g of ice by 1 degree celsius.

all help is appreciated ... thank you

[lakp]

oh, please lemme know if need clarifications . the explanation may be a but clumsy ... thank you (i dont see an edit button so i had to write a new post)

[Kdub]

well just re-arrange the equation...use mine to make is simple:
q = mcT                            q = heat
                                        m = mass
                                        c = specific heat
                                        T = change in temp

So just solve for c then...
c = q / (mT)

[lakp]

true, but the ice has not increased or decreased in temperature, which means I would be dividing by zero,

c=q/(mass X change in temp)

the change in temp of the ice is zero and i dont know whether to use the beginning mass of the ice or the end mass of the ice because the ice melted from 50 grams to 48 grams . the temp is still 0 degrees celsius ..

[xiankai]

then, u must be finding the specific latent heat of fusion, which is a different formula consisting of Q=ml_f

remember, ice has a specific heat capacity, AND a specific latent heat of fusion. do not confuse the two terms.

[lakp]

oooooooooooooooooooh!!! thank you thank you, I WAS confusing those two terms ...

so for your formula you said  Q=mlf
i dont know what the variables stand for ...

heat = mlf

if m=mass, what do l and f stand for?

[xiankai]

hmm my bad the f should be read as a subscript, such that the l stands for the latent heat of fusion

[Donaldson Tan]

specific heat capacity (c) is the amount of heat needed to raise/drop the temperature of a substance per unit mass.

specific latent heat of fusion (l_f)is the amount of heat needed to melt a substance per unit mass.

the melting point of a substance depends on the pressure. at 1atm, ice melts at 0 degree celcius. in order for melting to occur, you have to raise the temperature of ice to its melting point. the amount of energy needed in this process is given as Q = mc*dT. After you have raised the temperature to 0 degree celcius, all the heat u supply will be used for melting. The amount of heat required the ice is therefore Q = m*l_f

Since no process is 100% efficient, the amount of heat you need to melt the ice is therefore Q = m*c*dT + m*l_f (m: mass of ice, dT: change in temperature of ice just before melting)