A block of lead of heat capacity 1 kJ K−1 is cooled from 200 K to 100 K in two ways.
((a)) It is plunged into a large liquid bath at 100 K.
((b)) The block is first cooled to 150 K in one liquid bath and then to 100 K in another bath.
Calculate the entropy changes in the system comprising block plus baths in cooling from 200 K to 100 K in these two cases. Prove that in the limit of an infinite number of intermediate baths the total entropy change is zero.