If 425 joules are absorbed from the higher temperature reservoir and 295 joules of that is passed on to the lower temperature reservoir, how much work has been done by the system?

130 J

Explanation:

For the law of conservation of energy, the total energy absorbed by the hot reservoir must be equal to the sum of the energy passed to the cold reservoir and the work done by the system:

In this case, we have

So, the work done by the system is

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 .