The quantity of heat required to raise the temperature of a unit mass of a substance by 1 K is called:

According to the principle of calorimetry, heat lost by the hot object (copper ball) is equal to the heat gained by the cold object (water), assuming no heat loss to the surroundings.

$$Q_{lost, copper} = Q_{gained, water}$$ $$m_c c_c \Delta T_c = m_w c_w \Delta T_w$$

Given:

• Mass of copper ($m_c$) = $0.5 \text{ kg}$
• Initial temperature of copper ($T_{c,i}$) = $100 ^\circ\text{C}$
• Mass of water ($m_w$) = $0.2 \text{ kg}$
• Initial temperature of water ($T_{w,i}$) = $20 ^\circ\text{C}$
• Final steady temperature ($T_f$) = $35 ^\circ\text{C}$
• Specific heat capacity of water ($c_w$) = $4200 \text{ J/kg K}$

Calculate the change in temperature for copper ($\Delta T_c$):

$$\Delta T_c = T_{c,i} - T_f = 100 ^\circ\text{C} - 35 ^\circ\text{C} = 65 ^\circ\text{C}$$

Calculate the change in temperature for water ($\Delta T_w$):

$$\Delta T_w = T_f - T_{w,i} = 35 ^\circ\text{C} - 20 ^\circ\text{C} = 15 ^\circ\text{C}$$

$$(0.5 \text{ kg}) \times c_c \times (65 ^\circ\text{C}) = (0.2 \text{ kg}) \times (4200 \text{ J/kg K}) \times (15 ^\circ\text{C})$$ $$32.5 \text{ kg} \cdot ^\circ\text{C} \times c_c = 12600 \text{ J}$$ $$c_c = \frac{12600 \text{ J}}{32.5 \text{ kg} \cdot ^\circ\text{C}}$$ $$c_c \approx 387.69 \text{ J/kg K}$$

Rounding to a reasonable number of significant figures or checking the options, $388 \text{ J/kg K}$ is the closest.

The correct option is A.

$$\boxed{\text{A. } 388 \text{ J/kg K}}$$

3. The heat required to change $1 \text{ kg}$ of ice at $0 ^\circ\text{C}$ to water at the same temperature is called specific latent heat of fusion. This is the energy required for a phase change from solid to liquid without a change in temperature.

The correct option is B.

$$\boxed{\text{B. Specific latent heat of fusion}}$$

4. Radiation is the mode of heat transfer that does NOT require a material medium. It can transfer heat through a vacuum, such as the heat from the sun reaching Earth. Conduction and convection require a medium.

The correct option is C.

$$\boxed{\text{C. Radiation}}$$

5. According to the Kinetic Theory of gases, the pressure exerted by a gas is due to the collisions of the molecules with the walls of the container. As gas molecules move randomly, they frequently collide with the container walls, exerting a force that results in pressure.

The correct option is B.

$$\boxed{\text{B. Collisions of the molecules with the walls of the container}}$$