Suppose you have a classical system that consists of N particles moving in three dimensions. You calculate the entropy for the system using a phase space cell size ho and get the value So. a) Show that if you calculated the entropy using a cell size h₁ = ho/2, you would get the value S₁ = S₁ + 3Nk In2. b) Find the value you would get if you calculated the entropy using cell size aho, where a is a positive dimensionless constant.

Suppose you have a classical system that consists of N particles moving in three dimensions. You calculate the entropy for the system using a phase space cell size ho and get the value So. a) Show that if you calculated the entropy using a cell size h₁ = ho/2, you would get the value S₁ = S₁ + 3Nk In2. b) Find the value you would get if you calculated the entropy using cell size aho, where a is a positive dimensionless constant.