物理__熱學

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Enthaply of water at 25oC(hf) = 104.8kj/kg (steam table)
specific heat capacity of ice at -15oC is 2050 j/kgoC
mass of ice (m2) 50*2 = 100g = 0.1kg
mass of water(m1) = 0.2kg
heat Capacity for water (Cpw)= 4.2kj/kgK

Energy in water initially
m1hf = 104.8*0.2 = 20.96 kj

Energy in gain by ice (energy loss by water)
mCp(t2-t1) = 0.1*(2050)(0+15) = 3.075kj
(m1+m2)Cpw(t2-t1) = 0.3*4.2*(t2-0) = 1.26t2kj

Change in energy
20.96-3.075- 1.26t2 = (17.885-1.26t2) kj

[(17.885-1.26t2)/(m2+m1)/(Cpw)] = t2
(17.885-1.26t2)/(0.1+0.2)/4.2 = t2
14.19 - t2 = t2
14.19 = 2t2
t2 = 7.45oC

Heat given out by water when its temperature drops from 25'C to 0'C
= 0.2 x 4200 x 25 J = 21 000 J
Heat absorbed by ice should all 100 g of ice be melted
= 0.1 x (2050 x 15 + 334000 ) J = 36 475 J

Since the heat given out by water is not sufficient to melt all ice. There is still unmelted ice in the final mixture. The final temperature of the mixture is at 0'C.