Heating and Cooling Curves: Videos & Practice Problems

Heating and cooling curves illustrate the heat absorbed or released during phase changes. For water, key temperatures are 0°C (melting) and 100°C (boiling). During phase changes, temperature remains constant while average kinetic energy does not change, as heat converts to potential energy. The equations used are $q=m·c·\mathrm{\Delta T}$ for temperature changes and $q=m·\mathrm{\Delta H}$ for phase changes. Cooling curves represent exothermic processes where heat is released, leading to bond formation.

The Heating Curve

Heating and cooling curves are essential tools for understanding the heat absorbed or released during phase changes of substances, such as water. A heating curve illustrates how temperature changes over time as heat is added. For water, key temperatures to remember are 0 degrees Celsius, where it freezes or melts, and 100 degrees Celsius, where it begins to boil or condense. These temperatures are critical reference points, while for other substances, their specific melting and boiling points must be provided.

In a heating curve, the temperature remains constant during phase changes, indicated by flat segments on the graph. For water, below 0 degrees Celsius, it exists as a solid (ice). At 0 degrees Celsius, the solid begins to melt, transitioning into a liquid. This phase change occurs on a plateau where both solid and liquid coexist. Once all the ice has melted, the temperature of the liquid water begins to rise until it reaches 100 degrees Celsius, where it starts to boil, transitioning into gas (vapor). Again, during this phase change, the temperature remains constant until all the liquid has evaporated.

During phase changes, the average kinetic energy of the particles remains constant, as temperature does not change. However, the particles spread out more as they transition from solid to liquid to gas. The heat energy absorbed during these phase changes is converted into potential energy, which is the energy associated with the state of the substance. Solids have the lowest potential energy, liquids have higher potential energy, and gases have the highest potential energy.

In contrast, during temperature changes, heat energy is converted into kinetic energy, leading to an increase in average kinetic energy as the temperature rises. The relationship between heat energy (q), mass (m), specific heat capacity (c), and temperature change (ΔT) is expressed by the equation:

\( q = mc\Delta T \)

Here, ΔT is the difference between the final and initial temperatures. For water, it is important to remember that specific heat values differ depending on the phase: solid (ice), liquid (water), or gas (steam).

During phase changes, since temperature does not change, the equation simplifies to:

\( q = m \Delta H \)

Where ΔH represents the heat of fusion (melting) or heat of vaporization (boiling). The units for ΔH will determine whether mass (m) is measured in grams or moles. For example, if ΔH is given in joules per gram, then m should be in grams. The heating curve can be divided into segments: during the first segment, water transitions from solid to liquid (melting), while in the third segment, it transitions from liquid to gas (vaporization). Each segment where temperature changes uses the \( q = mc\Delta T \) equation, while segments involving phase changes use \( q = m \Delta H \).

Understanding these concepts is crucial for analyzing both heating and cooling curves, as the cooling curve simply represents the reverse process of the heating curve.

The Cooling Curve

The cooling curve represents the process of a substance losing heat, contrasting with the heating curve where heat is absorbed. Understanding the differences in phase changes is crucial. For instance, the transition from solid to liquid (melting) requires less energy compared to the transition from liquid to gas (vaporization). This is because, during melting, molecules are merely freed from their fixed positions but remain relatively close together. In contrast, vaporization necessitates that molecules be separated by significant distances, requiring more energy and time, which is reflected in the longer duration of the phase change on the heating curve.

In the context of the cooling curve, as a substance cools, it releases heat, resulting in a negative value for heat transfer (q). This exothermic process allows molecules to lose energy, slow down, and eventually bond together. For water, at 100 degrees Celsius, it can either vaporize or condense. The enthalpy of vaporization (ΔH_vap) is equal in magnitude but opposite in sign to the enthalpy of condensation (ΔH_cond), indicating that condensation is an exothermic process.

Similarly, at 0 degrees Celsius, water can either melt or freeze. The enthalpy of fusion (ΔH_fus) is directly related to the enthalpy of freezing (ΔH_freeze), with the latter being negative due to the formation of bonds during freezing. The relationships can be summarized as follows: ΔH_freeze = -ΔH_fus and ΔH_cond = -ΔH_vap.

In calculations involving these processes, the heat transfer can be expressed using the formula q = m × ΔH, where m is the mass and ΔH corresponds to the specific phase change (e.g., ΔH_cond for condensation and ΔH_freeze for freezing). Additionally, when temperature changes occur within a single phase, the formula q = mcΔT is used, where c represents the specific heat capacity of the substance in its respective phase (solid, liquid, or gas).

In summary, the key distinctions between heating and cooling curves lie in the direction of heat transfer and the associated energy changes. Heating curves involve endothermic processes with positive q values, while cooling curves involve exothermic processes with negative q values. Understanding these principles is essential for solving related problems and applying the concepts effectively.

Heating and Cooling Curves

To determine the energy required to convert 76.4 grams of acetone from a liquid at -30 degrees Celsius to a solid at -115 degrees Celsius, we need to consider the phase changes and temperature changes involved in the process. The melting point of acetone is -95 degrees Celsius, which is crucial for understanding the transitions between phases.

The process can be divided into three main segments: cooling the liquid acetone from -30 degrees Celsius to -95 degrees Celsius, the phase change from liquid to solid at -95 degrees Celsius, and finally cooling the solid acetone from -95 degrees Celsius to -115 degrees Celsius. Each segment will have its own heat calculation.

For the first segment, we calculate the heat lost (q₁) as the acetone cools from -30 degrees Celsius to -95 degrees Celsius using the formula:

q₁ = m * c_liquid * ΔT

where:

• m = mass of acetone = 76.4 g
• c_liquid = specific heat of liquid acetone (approximately 2.09 J/g°C)
• ΔT = final temperature - initial temperature = -95°C - (-30°C) = -65°C

Calculating this gives:

q₁ = 76.4 g * 2.09 J/g°C * (-65°C) = -10,726.6 J, or -10.7266 kJ.

Next, we consider the phase change (q₂) at -95 degrees Celsius, where the acetone freezes. The heat released during freezing can be calculated using the enthalpy of fusion:

q₂ = -n * ΔH_fusion

where:

• n = number of moles of acetone = 76.4 g / 58.08 g/mol = 1.31543 mol
• ΔH_fusion = 7.27 kJ/mol (the enthalpy of fusion, but negative for freezing)

Thus, we have:

q₂ = -1.31543 mol * 7.27 kJ/mol = -9.570 kJ.

Finally, we calculate the heat lost (q₃) as the solid acetone cools from -95 degrees Celsius to -115 degrees Celsius:

q₃ = m * c_solid * ΔT

where:

• c_solid = specific heat of solid acetone (approximately 1.67 J/g°C)
• ΔT = -115°C - (-95°C) = -20°C

Calculating this gives:

q₃ = 76.4 g * 1.67 J/g°C * (-20°C) = -2,521.2 J, or -2.5212 kJ.

To find the total heat (q_total) released during the entire process, we sum the three heat values:

q_total = q₁ + q₂ + q₃ = -10.7266 kJ - 9.570 kJ - 2.5212 kJ = -22.8178 kJ.

This negative value indicates that energy is released during the cooling and freezing process, confirming that the overall reaction is exothermic. Understanding these calculations is essential for analyzing phase changes and energy transfer in thermodynamic processes.

If 53.2kJ of heat are added to a 15.5g ice cube at - 5.00 ^oC, what will be the resulting state and temperature of the substance?

• A. 322.5°C, gas
• B. -3.70ºC, solid
• C. 98.82 ºC, liquid
• D. 222.5 ºC, gas

Answer: (A)

Here’s what students ask on this topic:

What is a heating curve and what does it represent?

A heating curve is a graphical representation that shows how the temperature of a substance changes as heat is added over time. It illustrates the phase transitions a substance undergoes, such as melting and boiling. For water, key temperatures are 0°C (melting point) and 100°C (boiling point). During phase changes, the temperature remains constant, indicating that the added heat is used to change the phase rather than increase the temperature. The curve typically includes segments where the substance is in solid, liquid, and gas phases, as well as flat plateaus where phase changes occur.

Why does the temperature remain constant during a phase change?

During a phase change, the temperature remains constant because the heat energy added to the system is used to break intermolecular bonds rather than increase the kinetic energy of the particles. This energy is converted into potential energy, which changes the state of the substance. For example, when ice melts at 0°C, the heat energy is used to break the bonds between water molecules in the solid state, turning them into liquid water, without changing the temperature.

What equations are used to calculate heat during temperature changes and phase changes?

During temperature changes, the equation used is:

$q=m\cdot c\cdot \Delta T$

where q is the heat added, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

During phase changes, the equation used is:

$q=m\cdot \Delta H$

where q is the heat added, m is the mass, and ΔH is the enthalpy change of the phase transition (e.g., enthalpy of fusion or vaporization).

What is the difference between a heating curve and a cooling curve?

A heating curve shows how the temperature of a substance increases as heat is added, illustrating endothermic processes where heat is absorbed. Key features include plateaus at phase change points where temperature remains constant. A cooling curve, on the other hand, shows how the temperature decreases as heat is removed, illustrating exothermic processes where heat is released. In a cooling curve, the substance releases heat, leading to bond formation, and the temperature also remains constant during phase changes. The equations used are similar but with opposite signs for the enthalpy changes.

Why does it take more energy to go from a liquid to a gas than from a solid to a liquid?

It takes more energy to go from a liquid to a gas than from a solid to a liquid because the molecules in a gas are much farther apart than in a liquid. In a liquid, molecules are still relatively close and only need enough energy to overcome the forces keeping them in a fixed position. However, to transition to a gas, molecules must be separated by much greater distances, requiring significantly more energy to overcome the intermolecular forces. This is why the plateau for vaporization on a heating curve is longer than that for melting.