Question

metal | specific heat (j/g°c)
cd | 0.232
cu | 0.385
fe | 0.450
ag | 0.235
10.0 g of each material has 100 j of energy added. which material has the smallest increase in temperature?
options: iron, silver, cadmium, copper

Explanation:

Step1: Recall the heat formula

The formula relating heat (\(q\)), mass (\(m\)), specific heat (\(c\)), and temperature change (\(\Delta T\)) is \(q = mc\Delta T\). We can rearrange it to solve for \(\Delta T\): \(\Delta T=\frac{q}{mc}\).

Step2: Identify constant values

Here, \(q = 100\space J\) (energy added) and \(m = 10.0\space g\) (mass of each metal) are constant for all metals. So \(\Delta T\) is inversely proportional to \(c\) (specific heat), i.e., the larger the specific heat, the smaller the temperature change.

Step3: Compare specific heat values

The specific heat values are: Cd (\(0.232\space J/g^\circ C\)), Cu (\(0.385\space J/g^\circ C\)), Fe (\(0.450\space J/g^\circ C\)), Ag (\(0.235\space J/g^\circ C\)). Among these, Fe has the largest specific heat (\(0.450\space J/g^\circ C\)).

Step4: Determine the smallest \(\Delta T\)

Since \(\Delta T\) is inversely proportional to \(c\) (when \(q\) and \(m\) are constant), the metal with the largest \(c\) will have the smallest \(\Delta T\). So Fe (iron) will have the smallest increase in temperature.

Answer:

iron