Question

When \(47.5 \mathrm{~J}\) of heat are added to \(13.2 \mathrm{~g}\) of a liquid, its temperature rises by \(1.72{ }^{\circ} \mathrm{C}\). What is the heat capacity of the liquid?

Short answer

The heat capacity of the liquid is approximately 2.092 J/g°C.

Step-by-step solution

Understand the concept of heat capacity

Heat capacity (C) is the amount of heat (q) needed to raise the temperature of an object by one degree Celsius or Kelvin. It is given by the formula: C = q / (m * ΔT), where q is the heat added, m is the mass of the substance, and ΔT is the change in temperature.

Identify the known values

We know the heat added (q) is 47.5 J, the mass of the substance (m) is 13.2 g, and the temperature change (ΔT) is 1.72 °C. We need to plug these values into the heat capacity formula.

Calculate the heat capacity

Insert the given values into the heat capacity formula to find the heat capacity of the liquid. C = q / (m * ΔT) = 47.5 J / (13.2 g * 1.72 °C)

Perform the calculation

Divide the heat energy by the product of the mass and the temperature change to obtain the heat capacity. C = 47.5 J / (13.2 g * 1.72 °C) = 47.5 J / (22.704 g °C) ≈ 2.092 J/g°C

Key concepts

Specific Heat Calculation

Specific heat capacity, often abbreviated as specific heat, is a fundamental concept in understanding how different substances respond to changes in temperature. It's the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin). The formula for specific heat calculation is given by:
\( c = \frac{q}{m \times \Delta T} \)
Where \( c \) is the specific heat capacity, \( q \) is the heat energy added, \( m \) is the mass of the substance, and \( \Delta T \) is the temperature change.Using the given exercise data:

• Heat energy (\( q \)) is 47.5 Joules.
• Mass (\( m \)) is 13.2 grams.
• Temperature change (\( \Delta T \)) is 1.72°C.

We can find the specific heat capacity of the liquid by plugging these values into the formula:
\( c = \frac{47.5 \text{ J}}{13.2 \text{ g} \times 1.72 ^{\circ}\text{C}} \approx 2.092 \text{ J/g}^{\circ}\text{C} \)
This value means that each gram of the liquid requires approximately 2.092 Joules of energy to raise its temperature by one degree Celsius.

Thermodynamics

Thermodynamics is the branch of physics concerning the relationships between heat, energy, work, and temperature. It is rooted in several fundamental laws:

• The zeroth law, which discusses thermal equilibrium.
• The first law, which equates heat transfer to changes in internal energy plus the work done (conservation of energy).
• The second law, suggesting the increase in the entropy, or disorder, of the universe.
• The third law, relating to the entropy of a system approaching a constant value as the temperature tends toward absolute zero.

In our exercise, we deal with the concept of heat energy transfer as a part of the thermodynamics field. When heat is added to a substance, part of that energy is used to increase the substance's internal energy, resulting in a temperature rise. Heat capacity is a way to quantify this aspect of thermodynamics; it tells us how much heat energy is required to change the temperature of a substance. Understanding thermodynamics allows us to predict and control these energy transfers in real-world applications, such as chemical processes, engines, and climate control systems.

Energy Transfer in Chemistry

Energy transfer in chemistry involves changes in the internal energy of substances during chemical reactions or changes in physical states. Heat is a form of energy that flows between systems due to a temperature difference and is a key component in chemical reactions. Endothermic reactions absorb heat from the surroundings, while exothermic reactions release heat.
In the context of the exercise, we're specifically looking at heat absorption. The liquid absorbs 47.5 Joules to experience a temperature increase, reflecting an intrinsic property of the substance—its heat capacity. Understanding these energy transfer mechanisms is crucial for chemists, who must control reaction temperatures and conditions to optimize yields and create safe laboratory and industrial environments. Proper calculation of specific heat and overall heat capacity ensures that chemical substances are used efficiently and safely, making this knowledge essential for developing sustainable practices and novel materials.