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A 5.10 g sample of iron is heated from 36.0 to 75.0 C. The amount of energy required is 89.5 J. The specific capacity of this sample of iron is...


A.) 17800 J/g C

B.)0.900 J/g C

C.)11.7 J/g C

D.) 0.450 J/g C

E.) 2.22 J/g C

Verified Answer :

premedchemist

This can be solved from the equation q = m C  ΔT Where q is the heat added, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
We can rearrange the equation to find the specific heat capacity
q/(mΔT) = C
q = 89.5 J     m = 5.10 g     ΔT = (75.0 °C - 36.0 °C) = 39 °C
(89.5J)/(5.10 g 39 °C) = 0.450 J/g°C

Answer: Option (D) is the correct answer.

Explanation:

The given data is as follows.

       mass = 5.10 g,            \(T_{1} = 36^{o}C\),

       \(T_{2} = 75.0^{o}C\),          q = 89.5 J

It is known that relation between heat energy and specific heat capacity is as follows.

                           q = \(mC \Delta T\)

Hence, putting the given values into the above formula to calculate specific heat capacity as follows.

                           q = \(mC \Delta T\)

                        89.5 J = \(5.10 g \times C (75 - 36)^{o}C\)

                        89.5 J = \(5.10 g \times C \times 39^{o}C\)

                              C = \(0.450 J/g ^{o}C\)

Thus, we can conclude that the specific capacity of this sample of iron is \(0.450 J/g ^{o}C\).

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