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Using the values for the heat of fusion, specific heat of water, and or heat vap

ID: 722213 • Letter: U

Question

Using the values for the heat of fusion, specific heat of water, and or heat vaporization, calculate the amount of heat energy in each of the following: a) joules to condense 125 g of steam at 100 degrees celsius and to cool the liquid to 15.0 degrees celsius; b) joules needed to melt a 525-g ice sculpture at 0 degrees celsius and to warm the liquid to 15.0 degrees celsius; c) kilojoules released when 85.0 g of steam condenses at 100 degrees C, cool the liquid, and freeze it at 0 degrees C; d) joules to warm 55.0 mL of water (density=1.00 g/mL) from 10.0 degrees C and vaporize it at 100 degrees C.

Explanation / Answer

Data:
heat of vaporization = 44 KJ/mol
heat of fusion = 333.55 KJ/Kg
sp. heat of water = 4.186 KJ/Kg.K

(a) you have 125 gm steam at 100 degC to be cooled to liquid water at 15 degC

125gm of steam = (125/18) = 6.944 moles of steam

phase change involved = steam at 100 deg C to liquid water at 100 degC
liquid water at 100 degC to liquid water at 15 degC

so total heat change will be sum of heat changes of these two transitions.

heat "is evolved" during phase change involved of steam at 100 deg C to liquid water at 100 degC = 6.944*(heat of vaporization) = 305.56 KJ
heat "is evolved" when liquid water cools from 100 to 15 degC = m*(sp.heat)*dT
m = 125gm=0.125Kg, sp.heat = 4.186 KJ/Kg.K, dT = 100-15 = 85K
heat lost = 44.48KJ

net heat "lost" = 305.56 + 44.48 = 350KJ (since heat is lost, you may put a negative sign if the same is followed by you as convention)

(b) 525gm ice at 0 degC to liquid water at 15 degC

again two changes are there: ice at 0 degC to liquid water at 0 degC

and, water at 0 degC to water at 15 degC

mass of ice/water = 525gm = 0.525kg

heat absorbed while first chage (ice->water) = (heat of fusion)*(mass of ice) = 0.525*333.55 = 175.11KJ

heat absorbed for second change = m*c*dT

we have m=0.525kg, c = 4.186 KJ/Kg.K, dT = 15K... put all values to get heat absorbed = 32.96KJ

net heat "absorbed" = 175.11+32.96 = 208.07KJ (since heat is gained, you may put a positive sign if the same is followed by you as convention)

(the procedure is same for all cases... for parts (c) and (d) I am writing the changes involved, heat released/absorbed can be calculated as demonstrated.

(c)

85 gm of steam at 100 degC to liquid water at 100 degC

heat is "lost" and is equal to (85/18)*(44) = 207.78KJ

next

85gm or 0.085kg of liquid water at 100 degC is cooled to 0 degC

heat lost = m*c*dT = 0.085*4.186*100 = 35.6KJ

next

85gm of liquid water has to be frozen to ice at 0 DegC

heat lost = 0.085*333.55 = 28.35KJ

net heat lost = 271.82KJ (-ve sign may apply as heat is lost)

(d)

as density is 1gm/ml , 55ml weighs 55gm or 3.056 mol or 0.055kg

heat added when this is heated from 10 degC to 100 degC

heat added = m*c*dT = 0.055*4.186*90 = 20.72KJ

heat added when 55gm or 3.056mol of water is vaporized to steam at 100 degrees = (3.056*44) = 134.44KJ

net heat added = 20.72+134.44 = 155.16 KJ (+ve sign may apply as heat is added)