When 10 kg of water at 27C is mixed with 10 kg of water at 5

When 1.0 kg of water at 27°C is mixed with 1.0 kg of water at 58°C in a well-insulated container, what is the change in entropy of the system.

Solution

Change in entropy

dS=2.303 m c log(T2/T1)

where

m=mass

c=specific heat

T1,T2=initial and final temperatures

To find T2

Heat lost by 1kg water=Heat gained by 1kg water

mcdT=constant

1x4200x(300-T2)=1x4200x(T2-331)

T2=315.5K

T1=300K

dS₁=2.303x1x4200xlog(315.5/300)=211.6 J/K

dS₂=2.303x1x4200xlog(315.5/331)=-201.46 J/K

net change in entropy=-10.14 J/K