6. A total of 135 J of work is done on a gaseous refrigerant as it undergoes compression. If the internal energy of the gas increases by 114 J during the process, what is the total amount
of energy transferred as heat? Has energy been added to or removed from the refrigerant as
heat?

Eh = 21 [J]

Removed as heat.

Explanation:

This is a case of energy conservation, we have to take into account the energies that go in and out of the system. In this case, 135 [J] of energy are entered in the form of work of the compressor to the chamber where the refrigerant is compressed, now of these 135 [J] 114 [J] were used as internal energy, this internal energy is used to increase the pressure and temperature of the refrigerant.

In this way the rest of the energy of the 135 [J] was lost in the form of heat to determine this loss of energy, we simply perform the arithmetic subtraction.

Eh = 135 - 114 = 21 [J]

Eh = 21 [J]

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 .