Heat

An important concept for understanding how heat is measured is the concept of heat capacity.

  Heat Capacity: amount of heat needed to raise an object's temperature by 1 degree Kelvin.

More specifically we define

  Molar Heat Capacity: amount of heat required to raise the temperature of one mole of a substance by one degree Kelvin.
  Specific Heat Capacity: amount of heat required to raise the temperature of one gram of a substance by one degree Kelvin.

The heat capacity can vary quite a bit, particularly for gasses, depending on whether the pressure or volume is held constant as heat is added. Therefore, we further distinguish the heat capacities with the following symbols:

  C_V: Molar Heat Capacity at constant volume.
  C_P: Molar Heat Capacity at constant pressure.
  C_S: Specific Heat Capacity at constant pressure.

Since most processes discussed in this course are carried out at a constant 1 atmosphere of pressure, we will emphasize C_S and C_P.

If we have n moles of a substance, the heat transferred and the corresponding change in temperature are given by

Alternatively, if we have m grams of a substance, the heat transferred and the corresponding change in temperature are given by

Below are the specific heats of some common substances

The specific heat of water is one of the highest known specific heats. It is several times higher than that of compounds like limestone (CaCO₃) and quartz (SiO₂), which are the major constituents of rocks. Water can absorb or give up large amounts of heat with a smaller change in temperature than rocks (CaCO₃, SiO₂, MgO). That's why temperature fluctuations are smaller near large bodies of water like the ocean or Lake Erie than someplace like the desert in Arizona.

A piece of iron with a mass of 72.4 grams is heated to 100°C and plunged into 100 grams of water that is initially at 10.0°C. Calculate the final temperature that is reached assuming no heat loss to the surroundings. The heat capacities of iron and water are C_s(H₂O) = 4.18 J/g-°C and C_s(Fe) = 0.449 J/g-°C.

First of all, we note that the heat gained by the cooler body + the heat lost by the warmer body = 0

In other words

q_H2O = - q_Fe

thus we write

m_H2O C_s(H₂O) ΔT_H2O = - m_Fe C_s(Fe) ΔT_Fe

at equilibrium we have

T_f(H₂O) = T_f(Fe)

so we solve for T_f

m_H2O C_s(H₂O) [ T_f - T_i (H₂O)] = - m_Fe C_s(Fe) [T_f - T_i(Fe)]

and obtain

The heat flow associated with a chemical reaction is experimentally measured using a device called a calorimeter.

Calorimetry:

the science of measuring heat flow (based on observing the temperature change when a body absorbs or discharges heat).

Consider a reaction that gives off energy to its surroundings

We know the energy given off by this reaction will be transferred to the surroundings as heat and work.

Now, from

we know that if we seal the reaction in a vessel strong enough then that the volume can't change, and thus there can be no work done by the reaction since ΔV = 0. In this case we will have

That is, all the energy will be transferred as heat into the surroundings. Therefore, if we surround our sealed chemical reaction container (i.e., our system) with substances of known heat capacity, then all we need to do is measure the temperature change of these surroundings to determine q (i.e., the heat evolved) and thus the total change in energy.

This is done in what is called a Bomb Calorimeter.

Bomb Calorimeter:

Calorimeter designed to measure heat flow with constant volume (no work is possible).

1.00 grams of N₂H₄, hydrazine, is burned in a bomb calorimeter

and the temperature of the calorimeter increases by 3.51°C. The bomb calorimeter has a heat capacity of 5.510 kJ/°C. What is the quantity of heat evolved?

What is the heat evolved per mole of N₂H₄?

Thus, we can finally write

We have measured an energy change of 618 kJ for this reaction (i.e., the heat evolved at constant volume). Remember that ΔU is a state function (unlike q), so this number is good regardless of the history of the reactants and products. That is, 1 mole of hydrazine will always react with 1 mole oxygen and give 618 kJ of energy.