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Answer to Question #26651 in Atomic and Nuclear Physics for nini

Question #26651
a copper calorimeter of mass 100kg contains 50g of water and 5g of ice at 0 degree celcius.what mass of steam at 100 degree celcius must be passed to the calorimeter to raise the temp to 30 degree celcius.
Expert's answer
Qs = Qw + Qc + Qi
Qs - lost by steam
Qw - gained by water
Qc - gained by copper
Qi - gained by ice

Qs = L*Ms + (100-30)*Cw*Ms
Qw = (30-0)*Cw*Mw
Qc = (30-0)*Cc*Mc
Qi = R*Mi + (30-0)*Cw*Mi
Ms, Mw, Mc, Mi - masses of steam, water, copper and ice
Cw=4200 J/(kg*K), Cc=385 J/(kg*K) - heat capacities of water and copper
L=2256 kJ/kg - evaporation heat of water
R=333 kJ/kg - heat of fusion of water

Q = Qw + Qc + Qi = (30-0)*Cw*Mw + (30-0)*Cc*Mc + R*Mi + (30-0)*Cw*Mi =
= 30*4200*0.05+30*385*100+30*4200*0.005+333000*0.005= 1163595 J
Q = Qs = L*Ms + (100-30)*Cw*Ms
Therefore:
Ms = Q/(L+70*Cw) = 1163595 J / ( 2256000+70*4200) J/kg = 1163595/(2256000+70*4200) kg = 0.456 kg = 456 g
Answer: 456 g

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