Water calorimetry

Water calorimetry measures an energy transfer using the thermal response of water. In radiation metrology, it determines absorbed dose to water from a small measured temperature rise. The ideal conversion follows from $Q=m{c}_w\Delta T$ and $D=Q/m$:where $c_w$ is water's specific heat capacity. The sample mass cancels because dose is energy per unit mass.^[ref]

For an original scale estimate, take $c_w=4180\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ as an illustrative near-room-temperature value. An absorbed dose of $1\mathrm{Gy}=1\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$ would then give only $1/4180\mathrm{K}$, about $0.239\mathrm{mK}$. Detecting such a small change requires careful thermometry and separation from background thermal drift.

The physical conversion also has chemical assumptions. Heat defect describes the fraction of absorbed energy that does not appear as heat because of radiation-induced chemical change. Thermal conduction, convection and sensor effects are additional measurement questions, rather than alternate names for that chemical correction. This makes water calorimetry an example of an apparently direct energy measurement whose interpretation still needs a well-defined model.

The heat defect in water calorimetry measures the fraction of absorbed energy that does not appear as heat because of radiation-induced chemical changes. Writing absorbed energy as $E_a$ and the energy appearing as heat as $E_h$, the convention used by Norman V. Klassen and Carl K. Ross isA positive value means less heat than the absorbed-energy equivalent; a negative value means the chemical response adds heat.^[ref]

If other thermal corrections are treated separately, the absorbed dose isAn illustrative $k_{\mathrm{HD}}=0.02$ means that $c_w\Delta T$ represents 98% of the dose, so the chemical correction multiplies that thermal estimate by $1/0.98$. The example fixes a sign convention; it is not a measured universal value for water.

The motivating evidence included variations with dissolved gases and comparison of radiolysis calculations with chemical measurements of hydrogen peroxide. Those tests address chemical energy accounting. An external heat leak or a drifting thermometer can also alter a temperature reading, but belongs to a different correction mechanism.^[ref]

The sealed-water calorimeter of Steve R. Domen is an apparatus for measuring absorbed dose through the radiation-induced temperature rise of a controlled water volume. Domen's 1994 design enclosed the inner water in a thin-walled cylindrical glass vessel about 110 mm long and 33 mm in diameter, immersed in a larger water bath. The vessel also acted as a barrier against convection.^[ref]

Two calibrated thermistors served as temperature sensors in opposite arms of a Wheatstone bridge, increasing the electrical response to their common temperature rise. The apparatus therefore connected a small thermal change to a measurable resistance change, rather than directly counting radiation events.^[ref]

A central experiment compared water fillings with different dissolved-gas conditions. The temperature response could change because radiation also drove chemical reactions, motivating investigation of the heat defect. This comparison illustrates a useful apparatus principle: controlling the geometry and reading the thermometer carefully does not, by itself, establish that every joule deposited in the water becomes measurable heat.^[ref]