Question

question 5 of 20
you have two rocks made of the same material that are at the same temperature. the first rock has half the mass of the second rock. how does the thermal energy of the two rocks compare?
a. the first rock has half as much thermal energy as the second rock.
b. the first rock has twice as much thermal energy as the second rock.
c. the second rock has four times the thermal energy of the second rock.
d. the rocks have the same amount of thermal energy.

Explanation:

Step1: Recall thermal - energy formula

The thermal energy $Q = mc\Delta T$, where $m$ is mass, $c$ is specific heat capacity, and $\Delta T$ is the change in temperature. Since the rocks are of the same material (so $c$ is the same) and at the same temperature (so $\Delta T$ is the same), $Q\propto m$.

Step2: Analyze the mass - energy relationship

Let the mass of the first rock be $m_1$ and the mass of the second rock be $m_2$, with $m_1=\frac{1}{2}m_2$. Then $Q_1 = m_1c\Delta T$ and $Q_2 = m_2c\Delta T$. Substituting $m_1=\frac{1}{2}m_2$ into the formula for $Q_1$, we get $Q_1=\frac{1}{2}m_2c\Delta T=\frac{1}{2}Q_2$.

Answer:

A. The first rock has half as much thermal energy as the second rock.