Final answer:
The total entropy change for the process is 1,891,500 J/°C.
Step-by-step explanation:
In this problem, we are given a 30 kg iron block and a 40 kg copper block, both initially at 80°C, which are dropped into a large lake at 15°C. The system eventually reaches thermal equilibrium, and we are asked to determine the total entropy change for this process.
The entropy change for each block can be calculated using the equation:
S = mcΔT,
where S is the entropy change, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of iron is approximately 450 J/kg°C, and the specific heat capacity of copper is approximately 390 J/kg°C. The change in temperature for both blocks is 80 - 15 = 65°C. Therefore, the entropy change for the iron block is:
Siron = (30 kg)(450 J/kg°C)(65°C) = 877,500 J/°C,
and the entropy change for the copper block is:
Scopper = (40 kg)(390 J/kg°C)(65°C) = 1,014,000 J/°C.
The total entropy change for the process is the sum of the entropy changes for the iron and copper blocks:
Total entropy change = Siron + Scopper = 877,500 J/°C + 1,014,000 J/°C = 1,891,500 J/°C.