the external pressure to counteract the internal one — no work is generated, and the heat energy that would have gone into it must instead contribute to the internal energy of the sample, including raising its temperature by an extra amount. The specific heat capacity obtained this way is said to be measured at constant volume (or isochoric) and denoted etc. The value of is usually less than the value of . This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume. Hence the heat capacity ratio of gases is typically between 1.3 and 1.67. Applicability The specific heat capacity can be defined and measured for gases, liquids, and solids of fairly general composition and molecular structure. These include gas mixtures, solutions and alloys, or heterogenous materials such as milk, sand, granite, and concrete, if considered at a sufficiently large scale. The specific heat capacity can be defined also for materials that change state or composition as the temperature and pressure change, as long as the changes are reversible and gradual. Thus, for example, the concepts are definable for a gas or liquid that dissociates as the temperature increases, as long as the products of the dissociation promptly and completely recombine when it drops. The specific heat capacity is not meaningful if the substance undergoes irreversible chemical changes, or if there is a phase change, such as melting or boiling, at a sharp temperature within the range of temperatures spanned by the measurement. Measurement The specific heat capacity of a substance is typically determined according to the definition; namely, by measuring the heat capacity of a sample of the substance, usually with a calorimeter, and dividing by the sample's mass. Several techniques can be applied for estimating the heat capacity of a substance, such as fast differential scanning calorimetry. The specific heat capacities of gases can be measured at constant volume, by enclosing the sample in a rigid container. On the other hand, measuring the specific heat capacity at constant volume can be prohibitively difficult for liquids and solids, since one often would need impractical pressures in order to prevent the expansion that would be caused by even small increases in temperature. Instead, the common practice is to measure the specific heat capacity at constant pressure (allowing the material to expand or contract as it wishes), determine