Question

Suppose that we replace the aluminum with a mystery metal and repeat the experiment in the video. As in the video, the mass of the metal is the same as that of the water. Room temperature is about 20 C before the start of the experiment. The water heats up to 40C, and the mystery metal heats up to 80C. Compared to that of water, the heat capacity of our mystery metal is

a)three times greater.
b) one-third as great.
c) half as great.
d) two times greater.
e) the same.

Please explain..

Answer 1

Concepts and reason

The concept required to solve this problem is heat capacity and heat absorbed in thermodynamic process.

Initially, obtain the temperature difference of both metal and water. Finally, obtain the expression for heat capacity of mystery metal in terms of heat capacity of water.

Fundamentals

The expression for absorption of heat is given by,

Here, is mass, is specific heat and is temperature difference.

The temperature difference is,

Here, is final temperature and is room temperature.

Heat capacity is given by,

Here, is the specific heat and is the mass.

The temperature difference of water is,

Here, is water temperature and is room temperature.

Substitute for and for in the above equation.

The temperature difference of metal is,

$AT=T-T $

Here, is metal temperature and is room temperature.

Substitute for and for in the above equation.

Heat absorbed by water is given by,

Heat absorbed by the metal is given by,

The net amount of heat absorbed is given by,

Substitute for and for in the above equation.

Therefore, the option (b) is correct.

Ans:

Compared to that of water, the heat capacity of mystery metal is one-third as great.