Consider the data about gold metal in Exercise 5.26(b). (b) Suppose that the same amount of heat is added to two 10.0-g blocks of metal, both initially at the same temperature. One block is gold metal, and one is iron metal. Which block will have the greater rise in temperature after the addition of the heat?

Verified step by step guidance

1. Identify the specific heat capacities of gold and iron. The specific heat capacity is a measure of the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius.
2. Understand that the amount of heat added ( ext{Q}) is the same for both metals and can be calculated using the formula ext{Q} = mc ext{Δ}T, where ext{m} is the mass, ext{c} is the specific heat capacity, and ext{Δ}T is the change in temperature.
3. Rearrange the formula to solve for ext{Δ}T, which gives ext{Δ}T = ext{Q} / (mc). This shows that the change in temperature is inversely proportional to the specific heat capacity when the mass of the metal and the amount of heat added are constant.
4. Compare the specific heat capacities of gold and iron. Since the specific heat capacity of gold is lower than that of iron, it requires less heat to raise the temperature of gold by one degree Celsius compared to iron.
5. Conclude that the gold block will have a greater rise in temperature than the iron block when the same amount of heat is added to both, due to its lower specific heat capacity.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. Different materials have different specific heat capacities, which means that for the same amount of heat added, some materials will experience a greater temperature change than others. In this case, comparing gold and iron will help determine which block experiences a greater rise in temperature.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. When heat is added to the two metal blocks, the energy will be distributed among the particles of each metal, affecting their temperature. Understanding how heat transfer works is essential to predict the temperature change in each block.

Thermal Equilibrium

Thermal equilibrium is the state reached when two objects in contact no longer transfer heat between them, as they are at the same temperature. In the context of this question, it is important to recognize that the initial conditions of both blocks are the same, and the final temperature will depend on their specific heat capacities. This concept helps in understanding how the temperature of each block will change after heat is added.