# What is calorimetry Why is it important

## Calorimeter for determining the specific heat capacities of liquids

The *Calorimetry* deals with the measurement of heat quantities. These measurements are based on temperature changes, which are used to determine the amount of heat converted.

### Experimental setup

The experimental setups used in calorimetry are called *calorimeter* (from the Latin word "calor", which means something like "warmth"). Using an external heat supply, calorimeters can determine specific heat capacities of substances, especially liquids. The measuring principle of such a measurement has already been explained in the article on specific heat capacity using the example of water. In the simplest case, this is a thermally insulated vessel so that the heat losses to the environment can be kept as low as possible. The heat supplied is via a heating coil that is immersed in the liquid for which the specific heat capacity is to be determined.

In addition, care should be taken to ensure that the liquid is heated evenly. Otherwise the temperature measuring device would only measure a point temperature that is not representative of the entire liquid. Without uniform heating, the temperature of the liquid in the vicinity of the heat source would be significantly higher than in the edge area. The liquid should therefore always be mixed thoroughly while it is being heated. This can be done by a *Magnetic stirrer* can be achieved. The calorimeter stands on a plate that generates a rotating magnetic field. This rotating field brings in *Magnetic fish *for rotation and thus mixes the liquid.

### Consideration of heat losses

The supplied heat must be determined as precisely as possible in calorimeters in order to keep the measurement uncertainties low. This can be done, for example, in that the heating takes place via an electrically operated heating coil. It is easiest when the electrical power is displayed directly from the power supply unit. The electrical power can also be determined via the voltage U applied to the heating coil and the current I flowing through it. The product of voltage and current gives the electrical power of the heating coil P = U⋅I, which is completely converted into heat output (= heat energy emitted per time). The amount of heat Q released within the operating time t is then finally obtained from the product of the electrical power P and the time t:

\ begin {align}

& Q = P \ cdot t ~~~ \ text {with} ~~~ P = U \ cdot I ~~~ \ text {follows:} \ [5px]

\ label {q}

& \ boxed {Q = U \ cdot I \ cdot t} \ [5px]

\ end {align}

In principle, very good thermal insulation can prevent the transfer of heat to the environment (at least for the duration of the experiment), but it cannot prevent the inside of the calorimeter from heating up. A certain part of the heat supplied by the heating coil is therefore always unintentionally transferred to the calorimeter and is not completely absorbed by the water! In principle, heat loss cannot be prevented. It is therefore important to consider such heat losses and to know what amount of heat is transferred to the calorimeter! This happens because the calorimeter's heat absorption is explicitly taken into account in the energy balance.

The thermal energy Q supplied within the time t_{t} During operation of the heating coil, both the substance to be examined (Q_{S.}) (*here*: Liquid) as well as the calorimeter (Q_{K}) transfer. Both the temperature of the liquid and the temperature of the calorimeter increase by a certain amount ΔT. Hence:

\ begin {align}

& Q_ \ text {t} = Q_ \ text {S} + Q_ \ text {K} \ [5px]

& Q_ \ text {t} = C_ \ text {S} \ cdot \ Delta T + C \ cdot \ Delta T ~~~~~ \ text {with} ~~~ C_ \ text {S} = c_ \ text { S} \ cdot m_ \ text {S} ~~~ \ text {follows:} \ [5px]

\ label {1}

& Q_ \ text {t} = c_ \ text {S} \ cdot m_ \ text {S} \ cdot \ Delta T + C \ cdot \ Delta T \ [5px]

\ end {align}

In it, Q denotes_{S.} the (absolute) heat capacity of the substance to be examined, which is also the product of the specific heat capacity c_{S.} and mass m_{S.} expresses. The (absolute) heat capacity of the heated part of the calorimeter is denoted by C.

With slow heating, the calorimeter will always assume the temperature of the liquid in it. With identical starting temperatures, the temperature change ΔT of the substance to be examined is therefore identical to that of the calorimeter (at least with that part of the calorimeter which heats up with the substance). Even with rapid heating, sooner or later an equilibrium temperature will be established between the calorimeter and the liquid and the same temperature change will have taken place. The temperature change can therefore be excluded from equation (\ ref {1}):

\ begin {align}

& Q_ \ text {t} = \ left (c_ \ text {S} \ cdot m_ \ text {S} + C \ right) \ cdot \ Delta T \ [5px]

\ end {align}

The heat capacity C of the calorimeter can be determined in advance by mixing experiments (see next section). In this way, the unknown specific heat capacity c_{S.} of the liquid based on the heat Q supplied_{t} and the temperature change ΔT can be determined relatively precisely:

\ begin {align}

& Q_ \ text {t} = \ left (c_ \ text {S} \ cdot m_ \ text {S} + C \ right) \ cdot \ Delta T \ [5px]

& \ frac {Q_ \ text {t}} {\ Delta T} = c_ \ text {S} \ cdot m_ \ text {S} + C \ [5px]

& \ frac {Q_ \ text {t}} {\ Delta T} - C = c_ \ text {S} \ cdot m_ \ text {S} \ [5px]

\ label {cs}

& \ boxed {c_ \ text {S} = \ frac {Q_ \ text {t}} {m_ \ text {S} \ cdot \ Delta T} - \ frac {C} {m_ \ text {S}}} \ \ [5px]

\ end {align}

This formula can be interpreted as follows: Under real conditions, the specific heat capacity of the liquid to be determined is c_{S.} around the term C / m_{S.} less than if incorrectly ideal conditions were assumed. For this theoretical ideal case that the calorimeter does not absorb any heat, C = 0 applies. This would then mean that in principle no heat is required to heat the calorimeter. The heat Q supplied_{t} The liquid to be heated would then actually benefit completely.

### Heat capacity of the calorimeter (water value)

### Definition: water value

Obviously, the consideration of the heat losses or the determination of the heat capacity C of the calorimeter is of essential importance if the specific heat capacities of liquids in calorimeters are to be determined as precisely as possible. The heat capacity C of a calorimeter is also often called *Water value* although historically this is not entirely correct. The water value was originally understood to be the mass of water that has the same heat capacity as the calorimeter.

For example, if a calorimeter has a heat capacity of C = 42 J / K, the water value is consequently W = 10 g, since that water mass has the same heat capacity of 42 J / K. This clearly means that the calorimeter behaves as if 10 g of water had to be heated in addition to the liquid to be examined. The conceptual distinction is hardly made today, however, so the term *Water value *in most cases (and also used as such in the following) synonymous with the term *Heat capacity of the calorimeter* is!

### Preliminary tests to determine the water value of a calorimeter

The water value C of a calorimeter can be determined in advance by mixing experiments with water. The heating coil remains switched off the entire time! For this purpose, any mass of water m_{1} placed in the calorimeter at room temperature. Then the calorimeter and its contents (stir bar, temperature sensor, heating coil, etc.) and the water in it should be left to their own devices for a while. In this way, any temperature differences that may exist can be compensated for. Finally, after a certain time, there is a common starting temperature T_{1} on (usually room temperature).

Now a second amount of water is m_{2} with increased temperature T_{2} added to the calorimeter. Thereupon there will be a common equilibrium temperature between water mass m_{1}, Water mass m_{2} and adjust the calorimeter. The system should be given some time again so that the temperatures can equalize. The temperature of the water will usually decrease somewhat while the temperatures are being equalized, and that of the calorimeter will increase as the calorimeter is heated by the warm water. The resulting mixed temperature T_{M.} is then measured. This now allows conclusions to be drawn about the heat capacity of the calorimeter.

For this purpose, the energy balance of warming is examined more closely. The entire system is ultimately heated by the warm water mass 2. This supplied heat Q_{2} is divided into an amount of heat Q_{1} which heats the cold water mass 1 and has a heat conversion Q_{K}heating the calorimeter. The specific heat emitted Q_{2} the water mass m_{2} is determined on the basis of the temperature difference between the initial state T._{2} and the resulting mixing temperature T_{M.} (Final state). The absorbed thermal energy Q_{1} the water mass 1 results in an analogous way. This also applies to the amount of heat Q absorbed_{K} of the calorimeter, where the as yet unknown heat capacity C occurs.

\ begin {align}

Q_2 & = Q_1 + Q_ \ text {K} \ [5px]

c_ \ text {w} \ cdot m_2 \ cdot (T_2-T_ \ text {M}) & = c_ \ text {w} \ cdot m_1 \ cdot (T_ \ text {M} -T_1) + C \ cdot (T_ \ text {M} -T_1) \ [5px]

\ end {align}

In it, c_{w} the specific heat capacity of the water with c_{w}= 4.187 kJ / (kg⋅K). Thus, the only unknown quantity in this equation is the sought after heat capacity C of the calorimeter (water value). After changing the equation above, the water value of the calorimeter can finally be determined from the other measured values as follows:

\ begin {align}

& \ boxed {C = c_ \ text {w} \ left (m_2 \ frac {T_2-T_ \ text {M}} {T_ \ text {M} -T_1} -m_1 \ right)} ~~~ \ text { Heat capacity of the calorimeter} \ [5px]

\ end {align}

The water value of the calorimeter determined in advance in this way can now be used in equation (\ ref {cs}) to determine the specific heat capacity of the liquid to be examined as precisely as possible.

*annotation*: According to the original meaning of the water value W - i.e. as an equivalent water mass that has the same heat capacity as the calorimeter - that quantity C would still be due to the specific heat capacity of the water c_{w} to share:

\ begin {align}

& \ boxed {W = m_2 \ frac {T_2-T_M} {T_M-T_1} -m_1} ~~~ \ text {water value (original meaning)} \ [5px]

\ end {align}

### Factors influencing the water value of the calorimeter

Note that the heat capacity C of the calorimeter is not a constant value! It depends on the following influencing factors:

**Capacity**: If, for example, the calorimeter is only half full with liquid during an experiment, the entire apparatus may not be heated. The heated mass of the calorimeter is lower and so is its water value.

**Test duration**: The duration of the experiment also influences the water value. In this way, more calorimeter mass can heat up over longer times than with shorter measurements. In this case, the heat capacity of the calorimeter will be greater.

**temperature**: In a similar way, the temperature at which the experiment is carried out also influences the heat capacity. Because at higher process temperatures, the heat flow to the calorimeter also increases. This means that the calorimeter can heat up more strongly in the same time and thus more calorimeter mass will also be affected by the warming - the water value increases. In extreme cases, high temperatures in combination with very long measurement leadthroughs can also cause heat to penetrate the calorimeter and thus be transferred to the environment!

Due to the above-mentioned influencing variables, the heat capacity of the calorimeter should be determined in advance under conditions similar to those that will later prevail during the actual measurement. This means in particular:

- similar filling quantities,
- similar temperatures,
- similar mixing times.

The heat capacity of a calorimeter is an EXPERIMENTAL heat capacity and not THE heat capacity of the calorimeter.

### Bomb calorimeter

A special type of calorimeter is the so-called*Bomb calorimeter*. With the help of a bomb calorimeter, the heat of combustion ("calorific value") of food is determined. The sample to be examined is first placed in a vessel, which is called*bomb* referred to as. The bomb is then filled with oxygen and placed under high pressure. This vessel bomb is then placed in a water bath inside the calorimeter. With the help of an ignition wire, the sample is then burned, similar to the ignition of a bomb, which gives this calorimeter its name. The heat released during the combustion of the sample (= energy content of the food) can then be calculated from the temperature increase in the water bath.

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