Atwo dimensional monatomic ideal gas has what average kinetic energy per molecule, kavg? (hint: a two dimensional monatomic gas has a different kavg than a regular monatomic ideal gas. a two dimensional gas means that the atoms can only move in the x and y direction, but not the z carnot refrigerator has a coefficient of performance of 10. if it is run instead as a heat engine, what is its corresponding thermal efficiency?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .