I'm new to physics and i just started studying energy and i have a question:

• Consider an object (mass m=2kg) dropped freely from a height h = 2m (there is no friction between object and air).

1. If potential energy mgh only belongs to object, so its energy is E = PE + KE + U according to the law of conservation of energy, we have: ΔE = ΔPE + ΔKE + ΔU = Wg + Q but Wg = 2102 = 40(J) and Q = 0 (because there is no friction between air and object) and ΔPE + ΔKE = 0 so ΔU = 40(J), so its internal energy changed (?) but I know this is wrong because the object volume and its tempurature don't change and U = f(V,T) Therefore, potential energy should belongs to system "object-earth"
2. If potential energy mgh belongs to system "object-earth", so why textbook often say that mgh is potential energy only belongs to object ? I am so confused about this problem. Hope that you can help me solve this problem

I'm new to physics and i just started studying energy and i have a question:

• Consider an object (mass m=2kg) dropped freely from a height h = 2m (there is no friction between object and air).

1. If potential energy mgh only belongs to object, so its energy is E = PE + KE + U according to the law of conservation of energy, we have: ΔE = ΔPE + ΔKE + ΔU = Wg + Q but Wg = 2102 = 40(J) and Q = 0 (because there is no friction between air and object) and ΔPE + ΔKE = 0 so ΔU = 40(J), so its internal energy changed (?) but I know this is wrong because the object volume and its tempurature don't change and U = f(V,T) Therefore, potential energy should belongs to system "object-earth"
2. If potential energy mgh belongs to system "object-earth", so why textbook often say that mgh is potential energy only belongs to object ? I am so confused about this problem. Hope that you can help me about this thing