What is, “Free” in Gibbs Free Energy?

The word, “Free” in Gibbs Free Energy can be often confusing and I will try to address this aspect in simplified manner. Enthalpy is the total heat content, which means the internal energy + the product of pressure and volume. However, all enthalpy is not available to do work. The reason is the entropy or disorder. Nature seems to prefer disorder in broader sense as it does not like to spend energy to arrange things (there may be symmetries and orderliness in local/system/surrounding context but in broader context, i.e. in the context of the universe/multiverse, the disorder wins). Some enthalpy is spent in entropy. The remaining is left to do work and because that is what is available to do work, it is called available energy or free energy.

Greatest Integer Function Problem and Solution

Hollow Prism Q and A

Question (one option correct type):

A beam of light passes through a hollow glass prism. Then,

A) the beam of light undergoes lesser but some dispersion compared to solid glass prism
B) the beam of light is totally internally reflected and does not come out through the opposite face
C) the beam of light does not undergo dispersion at all and comes out parallel to the incident ray
D) the beam of light undergoes angular deviation

Solution

When a ray enters glass slab from air and again goes away from the glass slab, the emerging ray is parallel to the incident ray. This means that ray 2 is parallel to ray 1. Further, ray 3 is parallel to ray 2. This means that ray 1 is parallel to ray 3.

Answer: C.

IIT JEE Maths: Coordinate Geometry

Solution to the problem with one option correct based on coordinate geometry appeared in JEE 2008 paper I.

IIT JEE 2011 Complex Numbers Solution

Solution to the problem from, "Complex Numbers" topic that came in IIT JEE 2011.