A42.5 g piece of aluminum (which has a molar heat capacity of 24.03 j/ocmol) is heated to 82.4oc and dropped into a calorimeter containing water (specific heat capacity of water is 4.18 j/goc) initially at 22.3oc. the final temperature of the water is 24.9oc. calculate the mass of water in the calorimeter. ignore significant figures for this problem.

Answer : The mass of water in the calorimeter is, 200.12 grams.

Explanation :

First we have to calculate the specific heat capacity of aluminum.

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

where,

= specific heat of aluminum =

= specific heat of water =

= mass of Al = 42.5 g

= mass of water = ?

= final temperature of water =

= initial temperature of Al =

= initial temperature of water =

Now put all the given values in the above formula, we get

Therefore, the mass of water in the calorimeter is 200.12 grams.

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 .