Question

two samples of pure naphthalene of masses 100g and 200g are heated through temperature difference of 10c and 20c respectively. what is the ratio of the heat energy absorbed by the smaller sample to that absorbed by the larger sample

Answer 1

The heat energy absorbed by the smaller sample is

$$Q_1 = m_1 c\Delta T_1$$

where $m_1 = 100g = 0.1kg$ is the mass of the smaller sample, $c$ is the specific heat capacity of naphthalene and $\Delta T_1 = 10\degree C$ is the temperature difference.

The heat energy absorbed by the larger sample is

$$Q_2 = m_2 c\Delta T_2$$

where $m_2 = 200g = 0.2kg$ is the mass of the smaller sample, and $\Delta T_2 = 20\degree C$ is the temperature difference.

Thus, the ratio is:

$$\dfrac{Q_1}{Q_2} = \dfrac{m_1 c\Delta T_1}{m_2 c\Delta T_2}=\dfrac{m_1 \Delta T_1}{m_2 \Delta T_2}\\ \dfrac{Q_1}{Q_2} = \dfrac{0.1\cdot10}{0.2 \cdot 20} = 0.25$$

Answer. 0.25.