# Which of the following (using specific heat capacity provided) would show the smallest...

## Question:

Which of the following (using specific heat capacity provided) would show the smallest temperature change upon gaining 200.0J of heat?

a. 50.0 g Al, CAl=0.903J/gC

b. 25.0g granite, Cgranite=0.79J/gC

c. 25.0g Ag, CAg=0.235J/gC

d. 25.0g Au, CAu=0.128J/gC

## Calculating Heat Transfer from Specific Heat

Assuming no phase transition, the amount of heat energy transferred, Q, can be calculated from the mass, m, of the substance, its specific heat capacity, c, and its temperature change ΔT using the following expression:

$$Q = mc ΔT$$

Given the amount of heat supplied, the temperature change can then be written in terms of the other quantities as:

$$ΔT = \frac{Q}{mc}$$

Thus, we can now calculate the temperature change of each substance after receiving 200 J of heat:

a)

$$ΔT = \frac{200 \ J}{(50.0 \ g)(0.903 \ J/g \cdot °C)} \\ = 4.43 \ °C \\$$

$$ΔT = 4.43 \ °C$$

b)

$$ΔT = \frac{200 \ J}{(25.0 \ g)(0.79 \ J/g \cdot °C)} \\ = 10.1 \ °C \\$$

$$ΔT = 10.1 \ °C$$

c)

$$ΔT = \frac{200 \ J}{(25.0 \ g)(0.235 \ J/g \cdot °C)} \\ = 34.0 \ °C \\$$

$$ΔT = 34.0 \ °C$$

d)

$$ΔT = \frac{200 \ J}{(25.0 \ g)(0.128 \ J/g \cdot °C)} \\ = 62.5 \ °C \\$$

$$ΔT = 62.5 \ °C$$

We can see that Al (choice A) will have the smallest temperature increase after receiving 200 J of heat. 