Question

What is the specific heat of a metal if 175 j are needed in order to increase the temperature of a 50. g sample from 25 âc to 50. âc? report your answer with two significant figures.

Answer 1

Taking into account the definition of calorimetry, the specific heat of the metal is 0.14 $\frac{J}{gC}$.

Calorimetry

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).

So, the equation that allows to calculate heat exchanges is:

Q = c× m× ΔT

where:

Q is the heat exchanged by a body of mass m.

c is specific heat substance.

ΔT is the temperature variation.

In this way, between heat and temperature there is a direct proportional relationship (Two magnitudes are directly proportional when there is a constant so that when one of the magnitudes increases, the other also decreases; and the same happens when either of the two decreases .).

The constant of proportionality depends on the substance that constitutes the body and its mass, and is the product of the specific heat by the mass of the body.

Specific heat of the metal

In this case, you know:

• Q= 175 J
• m= 50 g
• c= ?
• ΔT= Tfinal - Tinitial= 50 C - 25 C= 25 C

Replacing in the expression to calculate heat exchanges:

175 J= c× 50× 25 C

Solving:

c=$\frac{175 J}{50 gx25C}$

c=0.14 $\frac{J}{gC}$

Finally, the specific heat of the metal is 0.14 $\frac{J}{gC}$.

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