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# Calorimeter

A calorimeter is a device used for calorimetry, the science of measuring the heat of chemical reactions or physical changes. The word calorimeter is derived from calorie, a unit of heat.

 Contents

## Example

A simple calorimeter may just consist of a thermometer attached to an insulated container. To find the enthalpy change per mole of a substance X in a reaction between two liquids X and Y, they are added to the calorimeter and the initial and final (after the reaction has finished) temperatures are noted. Multiplying the temperature change by the mass and specific heat capacities of the liquids gives a value for the energy given off during the reaction (assuming the reaction was exothermic.) Dividing the energy change by how many moles of X were present gives its enthalpy change of reaction.

## Types

### Constant-volume

A constant-volume calorimeter is a calorimeter in which the chemical reaction occurs within a rigid vessel whose volume cannot change. Bomb calorimeters are constant-volume calorimeters capable of withstanding the large pressure and force of explosive reactions.

#### Oxygen Bomb Calorimetry

A bomb calorimeter is a type of constant-volume calorimeter capable of withstanding the large pressure and force of explosive reactions.

Inevitably there will always be some heat loss from a calorimeter. One method of accounting for this is to use an electrical heater to produce the same temperature change over the same time period in the calorimeter as the reaction being measured. The electrical energy supplied to produce the temperature change is equal to the energy change that occurred in the reaction. Another method is to keep the temperature of the water surrounding the reaction vessel constant by heating or cooling it, and to measure the energy that is required to do this. This can then be used in calculations to produce extremely accurate results for energy changes.

### Constant-pressure

A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant.

An example is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and holes through which a thermometer and a stirring rod can be inserted. The inner cup holds the solution in which the reaction occurs, and the outer cup provides insulation.

### Differential scanning calorimeter

In a differential scanning calorimeter (DSC), heat flow into a sample—usually contained in a small aluminum capsule or 'pan'—is measured differentially, i.e. by comparing it to the flow into an empty reference pan.

Both pans sit on a small slab of material with a known (calibrated) heat resistance K. The temperature of the calorimeter is raised linearly with time (scanned), i.e. the heating rate dT/dt = β is kept constant. This time linearity requires good design and good (computerized) temperature control.

Heat flows into the two pans by conduction. The flow of heat into the sample is larger because of its heat capacity Cp. The difference in flow dq/dt induces a small temperature difference ΔT across the slab. This temperature difference is measured using a thermocouple. The heat capacity can in principle be determined from this signal:

$\Delta T = K {dq\over dt} = K C_p\, \beta$

Note that this formula (equivalent to Newton's law of heat flow) is analogous to, and much older than, Ohm's law of electric flow: ΔV = R dQ/dt = R I.

When a sudden change in the heat capacity occurs (e.g. when the sample melts), the signal will respond and exhibit a peak. From the integral of this peak the enthalpy of melting can be determined, and from its onset the melting temperature.

Differential scanning calorimetry is a workhorse technique in many fields, particularly in polymer characterization.

A modulating differential scanning calorimeter is a type of DSC in which a small oscillation is imposed upon the otherwise linear heating rate. This has a number of advantages. It increases sensitivity, allowing slow scans. It facilitates the direct measurement of the heat capacity in one scan. It also permits the simultaneous measurement of heat effects that are reversible and not reversible at the timescale of the oscillation. (reversing and non-reversing heat flow resp.)

### Isothermal titration calorimeter

In an isothermal titration calorimeter, the heat of reaction is used to follow a titration experiment. This permits determination of the end point (stoichiometry) of a reaction as well as its enthalpy.

The technique is gaining in importance particularly in the field of biochemistry, because it facilitates determination of substrate binding to enzymes.

### X-ray Microcalorimeter

In 1982, a new approach to non-dispersive X-ray spectroscopy, based on the measurement of heat rather than charge, was proposed by Moseley et al. (1984). The detector, and X-ray microcalorimeter, works by sensing the heat pulses generated by X-ray photons when they are absorbed and thermalized. The temperature increases indicates the photon energy. This invention combines high detector efficiency with high energy resolution. Any microcalorimeter must have a low-heat-capacity mass to absorb incident X-ray photons, a weak link to a low-temperature heat sink which provides the thermal isolation needed for a temperature rise to occur, and a thermometer to measure change in temperature.