Question

substance | specific heat (j/g°c)
aluminum | 0.900
copper | 0.385
iron | 0.450
granite | 0.790
25.0 g of each material has 150 j of energy added. which material has the largest increase in temperature?
options: copper, granite, aluminum, iron

Explanation:

Step1: Recall the heat formula

The formula for heat energy is \( Q = mc\Delta T \), where \( Q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat, and \( \Delta T \) is the change in temperature. We need to solve for \( \Delta T \), so rearranging the formula gives \( \Delta T=\frac{Q}{mc} \).

Step2: Identify given values

We know that \( Q = 150\space J \), \( m = 25.0\space g \) for each substance, and we have the specific heat \( c \) for each substance from the table.

Step3: Calculate \( \Delta T \) for each substance

• For aluminum: \( c = 0.900\space J/g^\circ C \)

\( \Delta T_{aluminum}=\frac{150}{25.0\times0.900}=\frac{150}{22.5}\approx6.67^\circ C \)

• For copper: \( c = 0.385\space J/g^\circ C \)

\( \Delta T_{copper}=\frac{150}{25.0\times0.385}=\frac{150}{9.625}\approx15.6^\circ C \)

• For iron: \( c = 0.450\space J/g^\circ C \)

\( \Delta T_{iron}=\frac{150}{25.0\times0.450}=\frac{150}{11.25}\approx13.3^\circ C \)

• For granite: \( c = 0.790\space J/g^\circ C \)

\( \Delta T_{granite}=\frac{150}{25.0\times0.790}=\frac{150}{19.75}\approx7.60^\circ C \)

Step4: Compare the temperature changes

Comparing the calculated \( \Delta T \) values: \( 15.6^\circ C \) (copper) > \( 13.3^\circ C \) (iron) > \( 7.60^\circ C \) (granite) > \( 6.67^\circ C \) (aluminum). So copper has the largest increase in temperature.

Answer:

A. copper