No. Mechanical energy is not conserved. There's quite a bit of friction on the slide. So some of the potential energy is lost to heat on the way down, and the child arrives at the bottom with hot pants and less kinetic energy than you might expect.
Answer:

Work done = = 5 kJ
Explanation:
Given data:
volume of nitrogen 



Polytropic exponent n = 1.4
![\frac{T_2}{T_1} = [\frac{P_2}{P_1}]^{\frac{n-1}{n}](https://tex.z-dn.net/?f=%5Cfrac%7BT_2%7D%7BT_1%7D%20%3D%20%5B%5Cfrac%7BP_2%7D%7BP_1%7D%5D%5E%7B%5Cfrac%7Bn-1%7D%7Bn%7D)
putting all value
![\frac{T_2}{473} = [\frac{80}{150}]^{\frac{1.4-1}{1.4}](https://tex.z-dn.net/?f=%5Cfrac%7BT_2%7D%7B473%7D%20%3D%20%5B%5Cfrac%7B80%7D%7B150%7D%5D%5E%7B%5Cfrac%7B1.4-1%7D%7B1.4%7D)

polytropic process is given as



work done 

= 5 kJ
C, they didn't know any better