A 40-g block of ice is cooled to -68 degree C and is then added to 590 g of wate

Question

A 40-g block of ice is cooled to -68 degree C and is then added to 590 g of water in an 80-g copper calorimeter at a temperature of 23 degree C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to 0degree C, melt, and then continue warming as water. (The specific heat of ice is 0.500 cal/g middot degree C = 2,090 J/kg middot degree C.) Your response differs from the correct answer by more than 10%. Double check your calculations.degree C

Explanation / Answer

Here Q1 + Q2 + Q3+ Q4+Q5 = 0 OR may not be 0

Q1 is the quantity of heat for ice

Q2 heat for ice to melt

Q3 heat of warm water

Q4 energy coming out of copper

Q5 energy coming out of water

NOW WE HAVE TO CHECK THE VALUES OF

Q1 + Q2 = -Q4 - Q5

(heat is added) = ( heat taken away)

if L.H.S > RHS ,then ice didnt melt

if L.H.S < RHS, ice didnt melt and cold water warms up

where Q2 is the phase change

from the table , L.H.S is greater ,and so ice is left

Q1 = MASS * SPECIFIC HEAT * CHANGE IN TEMP

= 0.04 * 2090*68

= 5684.8J

Q2 = mass*latent heat

= 0.04 *333000

= 13320 J

let p = Q1 + Q2

= 5684.8J + 13320 J

   = 19004.8

Q4 = -56804.02

Q5 = 712.08

- (Q4 +Q5) = -(-56091.94) J

   = + 56091.94 J

IN isolated system ,

   Q3+ Q4 + Q5 = -(Q1+ Q2)

   = -p

and let k = (mass of warm water * specific heat of warm water ) + (mass of copper *specific heat of copper)

   =0.590* 4186 + 0.08 * 387

k= 2500.7

Calculating for temperature final we have,

   Tf = (-p / k + T i of warm water) / [( mass of ice * specific heat of ice / k ) + 1 )]

   substituting the values we get,

Tf = [(-19004.8/2500.7 ) + 23] / [(0.04*4186/2500.7) + 1]

   = 15.400 / 1.066957

   = 14.433571 degrees c

hence the final temp = 14.4335 C

part 2:

to find the mass of ice left,

ice did not melt so ,

Q1 +Q2+Q4+Q5 =0

Q2 IS THE phase change

Q2 = mass of phase * latent heat

final temperature =0

mass of phase = mass of ice left

therefore mass of ice left = mice = (-Q1-Q4-Q5) /L

   = (-5684.8J + 56091.94 J) / 333000

= 0.1513 Kg

= 151.372 g

ICE MELT COLD WATER WARM WATER COPPER M 0.04 0.04 0.04 0.590 0.08 C 2090 4186 4186 387 Tf 0 ? it may or may not be zero it may or may not be zero Ti -68 0 23 23 dT 68 ? -23 23 L NA 333000 NA NA NA

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