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# How do i calculate the amount of heat absorbed and heat lost with the mass, volume, and two temp. given?

A 22.5 gram piece of an unknown metal is heated to 100 degree C then transferred quickly and without cooling into 100 mL of water at 20 degree C. The final temperature reached by the system is 26.9 degree C.

a) Calculate the quantity of heat absorbed by the water. show all work.

b) Determine the quantity of heat lost by the piece of metal. Show all work

c) Calculate the specific heat of a metal in J/g degree C. show all work

### 2 Answers

- billrussell42Lv 71 decade agoFavorite Answer
Assuming the water is covered and insulated so that no heat is lost.

Specific heat capacity of water 4.184 J/(g·K)

density of water 0.998 g/cm³

The temperature of the water goes up by 6.9º

Weight of water is calculated from volume and density

Volume = 100mL or 100cm³

weight is 100cm³ x 0.998 g/cm³ or 99.8g

Energy in J imparted to the water is calculated from the Specific heat

energy = 99.8g x 6.9º x 4.184 J/(g·K) = 2881 J

(formula from dimensional analysis, as all these are)

Given the conditions, this is also the amount of heat lost by the piece of metal.

Specific heat of the metal, in J/(g·K) calculation.

The metal loses 100-26.9 = 70.1º

Specific heat = 2881 J / 22.5 g x 70.1º = 908 J/(g·K)

(J/(g·K) is same as J/(g·C)

In case you are not familiar:

Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. It is routinely used by physical scientists and engineers to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena.

Basically it is used to check that you have an equation, with actual measurements, correct. Write all the units down, and cancel and combine them, and the result should have the correct units for the answer.

Or if you are unsure how to combine measurements to get the answer desired, arrange the elements of the calculation so that the units combine to form the desired result.

take an example.

Specific heat has units of J/(g·K).

I have one quantity of energy in J, a temperature in C (same as K) and a weight in grams.

So if I take the energy and divide it by the temp and weight, I'll get the correct units.

- Anonymous5 years ago
Due To Change in Specific heat Capacity of the Objects