AP Chemistry 6.3-6.4: Heat Transfer and Calorimetry

Thermal energy

Thermal energy is the kinetic energy associated with the random motion of the atoms and molecules in matter.

Temperature

Temperature quantitatively indicates how hot or cold a sample is and is related to the average kinetic energy of its particles. It does not directly measure the total thermal energy, which also depends on the amount of matter.

How are thermal energy and temperature related when no phase change or chemical reaction occurs?

Adding thermal energy generally increases temperature, while removing thermal energy decreases temperature. The relationship depends on the substance's mass and specific heat.

Heat ($q$)

Heat is the transfer of thermal energy between bodies at different temperatures. It spontaneously transfers from the hotter body to the cooler body until thermal equilibrium is reached.

Thermal equilibrium

Thermal equilibrium occurs when objects in thermal contact reach the same temperature. At that point, there is no net heat transfer between them.

Why does heat flow spontaneously from a hot object to a cold object?

Particles in the hotter object have greater average kinetic energy, and collisions transfer energy to particles in the cooler object. The net transfer continues until both objects have the same temperature.

Exothermic process

An exothermic process releases heat from the system to the surroundings, so $q_{\text{system}}<0$. Combustion is a common example.

Endothermic process

An endothermic process absorbs heat from the surroundings into the system, so $q_{\text{system}}>0$. Dissolving certain salts in a cold pack is an example.

How do the signs of $q$ and the temperature change of a substance relate?

For a substance being analyzed, $q>0$ means it gains thermal energy and usually warms, while $q<0$ means it loses thermal energy and usually cools. Phase changes can involve heat transfer without a temperature change.

What are the SI units and useful conversions for heat and energy?

The SI unit is the joule (J), where $1\ \text{J}=1\ \text{kg}\,\text{m}^2/\text{s}^2$; $1\ \text{kJ}=1000\ \text{J}$. The calorie is related by $1\ \text{cal}=4.184\ \text{J}$, and a food Calorie is $1\ \text{kcal}$.

Heat capacity ($C$)

Heat capacity is the heat required to change the temperature of an entire object by one degree: $C=\dfrac{q}{\Delta T}$. It is an extensive property because it depends on both the substance and the amount present.

Specific heat capacity ($c$)

Specific heat is the heat required to raise the temperature of one gram of a substance by one degree: $c=\dfrac{q}{m\Delta T}$. It is an intensive property that depends on the substance, not the sample size.

How are heat capacity and specific heat related?

For a sample of mass $m$, $C=mc$. A larger sample of the same material has a larger heat capacity but the same specific heat.

Molar heat capacity

Molar heat capacity is the heat capacity per mole of a substance. Its typical units are $\text{J mol}^{-1}\,^{\circ}\text{C}^{-1}$ or $\text{J mol}^{-1}\,\text{K}^{-1}$.

Why does water require relatively large amounts of heat to change temperature?

Liquid water has a relatively high specific heat, about $4.184\ \text{J g}^{-1}\,^{\circ}\text{C}^{-1}$. Therefore, a given mass of water requires more energy for a specified temperature change than most metals.

Heat-temperature relationship for a substance

The heat transferred is calculated with $q=mc\Delta T=mc(T_{\text{final}}-T_{\text{initial}})$. This assumes the specific heat remains approximately constant and no phase change occurs.

How can the equation $q=mc\Delta T$ be rearranged to determine an unknown quantity?

Use $c=\dfrac{q}{m\Delta T}$, $m=\dfrac{q}{c\Delta T}$, or $\Delta T=\dfrac{q}{mc}$. Keep units consistent, such as grams, joules, and $^{\circ}\text{C}$.

Why is a temperature difference in degrees Celsius numerically equal to the same difference in kelvins?

The Celsius and kelvin scales have the same size unit interval; they differ only in the location of zero. Thus, $\Delta T$ has the same numerical value in $^{\circ}\text{C}$ and K.

A sample of $800\ \text{g}$ of water warms from $21\ ^{\circ}\text{C}$ to $85\ ^{\circ}\text{C}$. How much heat does it absorb?

Using $q=mc\Delta T$ with $c=4.184\ \text{J g}^{-1}\,^{\circ}\text{C}^{-1}$ and $\Delta T=64\ ^{\circ}\text{C}$, $q=(800)(4.184)(64)\approx2.1\times10^5\ \text{J}$, positive because the water absorbs heat.

An unknown $348\ \text{g}$ metal absorbs $6.64\ \text{kJ}$ and warms from $22.4\ ^{\circ}\text{C}$ to $43.6\ ^{\circ}\text{C}$. What is its specific heat, and what material does it resemble?

Using $c=\dfrac{q}{m\Delta T}$, $c=\dfrac{6640\ \text{J}}{(348\ \text{g})(21.2\ ^{\circ}\text{C})}=0.900\ \text{J g}^{-1}\,^{\circ}\text{C}^{-1}$. This value is close to aluminum.

Calorimetry

Calorimetry measures heat transfer by allowing a process to exchange energy with a calibrated object or medium and measuring the resulting temperature change.

System and surroundings in calorimetry

The system is the substance or reaction being studied. The surroundings include everything else that can exchange heat with the system, including the solution, calorimeter, and possibly the external environment.

What happens in a calorimeter during an exothermic reaction in solution?

The reaction system releases heat, which is absorbed by the solution and possibly the calorimeter, causing their temperature to increase. For the reaction, $q_{\text{system}}<0$.

What happens in a calorimeter during an endothermic reaction in solution?

The reaction system absorbs heat from the solution and calorimeter, causing the surroundings' temperature to decrease. For the reaction, $q_{\text{system}}>0$.

Energy balance for an ideal calorimetry experiment

If no heat escapes to the external environment, energy is conserved within the calorimeter: $q_{\text{system}}+q_{\text{surroundings}}=0$. Therefore, $q_{\text{system}}=-q_{\text{surroundings}}$.

How can the heat absorbed by a calorimeter solution be calculated?

If the solution's mass and specific heat are known, calculate $q_{\text{solution}}=m_{\text{solution}}c_{\text{solution}}\Delta T$. Then, under ideal conditions, the reaction heat is $q_{\text{reaction}}=-q_{\text{solution}}$.

How is the heat absorbed by a calorimeter accounted for in a calorimetry calculation?

If the calorimeter has a known heat capacity, calculate $q_{\text{cal}}=C_{\text{cal}}\Delta T$. For an insulated experiment, $q_{\text{system}}+q_{\text{solution}}+q_{\text{cal}}=0$.

What is a constant-pressure, or coffee-cup, calorimeter?

A constant-pressure calorimeter is typically an insulated cup open to the atmosphere. For a process carried out at constant pressure, the heat transferred to or from the system is $q_p$, which equals the enthalpy change, $\Delta H$, when only pressure-volume work is considered.

What is a constant-volume, or bomb, calorimeter?

A bomb calorimeter is a sealed, rigid vessel with constant volume. Because the volume cannot change, no pressure-volume work occurs, and the heat measured corresponds to the system's change in internal energy: $q_v=\Delta E$.

Why are calorimeters designed to be well insulated?

Insulation minimizes heat exchange with the external environment, so the measured temperature change more accurately reflects heat transfer between the reaction and the calorimeter's internal surroundings.

How does a coffee-cup calorimeter differ from a more advanced calorimeter?

A coffee-cup calorimeter is inexpensive and simple but allows more heat exchange with the environment, reducing accuracy. Research-grade calorimeters are more thoroughly insulated and use precise temperature sensors and controlled stirring.

Why does a calorimeter require calibration or a known heat capacity?

The temperature change depends on the heat capacity of all components absorbing energy, including the solution and calorimeter. Calibration allows the measured temperature change to be converted into an accurate heat value.