question: If molecules are packed more tightly together in solids than in liquids, why is it that solids can be compressed and liquids cannot?
comment: Liquids can be compressed. Incompressible liquid is a common assumption to make for certain flow calculations because for example the compressibility of water in a river has virtually no impact on the flow. In high pressure hydraulic systems the compressibility of the oil can be important
passages: "Given any x and any y, if all the molecules in y are perfectly elastic and spherical, possess equal masses and volumes, have negligible size, and exert no forces on one another except during collisions, then if x is a gas and y is a given mass of x which is trapped in a vessel of variable size and the temperature of y is kept constant, then any decrease of the volume of y increases the pressure of y proportionally, and vice versa."
   BULLET::::3. When a liquid boils it turns into a gas. The resulting gas takes up far more space than the liquid did.
   The easiest way to get an equation of state linking "P" and "V" is to assume that "K" is constant, that is to say, independent of pressure and deformation of the solid, then we simply find the Hooke's law. In this case, the volume decreases exponentially with pressure. This is not a satisfactory result because it is experimentally established that as a solid is compressed, it becomes more difficult to compress. To go further, we must take into account the variations of the elastic properties of the solid with compression.
   In order to increase energy density, some systems may use gases that can be liquified or solidified. "CO offers far greater compressibility than air when it transitions from gaseous to supercritical form."
  
  Section::::Emissions.
   Liquids and gases cannot bear steady uniaxial or biaxial compression, they will deform promptly and permanently and will not offer any permanent reaction force. However they can bear isotropic compression, and may be compressed in other ways momentarily, for instance in a sound wave.
   Where "M" is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure i.e. they are both Ideal gases. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 L under those same conditions.
  
  Section::::Temperature dependence.
   Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). In solids particles are closely packed. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice) or irregularly (an amorphous solid such as common window glass), and are typically low in energy. Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because in gases molecules are loosely packed.
   On the other hand, liquids have little compressibility. Water, for example, will compress by only 46.4 parts per million for every unit increase in atmospheric pressure (bar). At around 4000 bar (400 megapascals or 58,000 psi) of pressure at room temperature water experiences only an 11% decrease in volume. Incompressibility makes liquids suitable for transmitting hydraulic power, because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression.
   BULLET::::3. We are ignoring the "free volume" due to molecular disorder in liquids and amorphous solids as compared to crystals. This, and the assumption that monomers and solute molecules are really the same size, are the main "geometric" approximations in this model.
  
  BULLET::::4. For a real synthetic polymer, there is a statistical distribution of chain lengths, so formula_20 would be an average.
   Section::::In polymer science.
   The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10 bar (1 bar = 0.1 MPa) and a typical thermal expansivity is 10 K. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
   where "p" is the pressure of the gas, "T" is its temperature, and formula_9 is its molar volume. In the case of an ideal gas, the compressibility factor "Z" is equal to unity, and the familiar ideal gas law is recovered:
  
  "Z" can, in general, be either greater or less than unity for a real gas.
   The density of both gases and liquids depends on the pressure and temperature of the fluid. Thus volumes measured in cold conditions or in pressurised conditions will be lower than the same mass of fluid at warmer or depressurised conditions. This fact gives rise to the necessity of choosing a benchmark pressure and temperature in which all 'net' volumes will be expressed.
  
  Section::::Ideal gas law.
   Consider the difference between a carrot and chewed bubble gum. The carrot will stretch very little before breaking. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.
  
  Section::::Design terms.
   Like the specific heat, measured the molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities.
   In gases, adiabatic compressibility is directly related to pressure through the heat capacity ratio (adiabatic index), while pressure and density are inversely related to the temperature and molecular weight, thus making only the completely independent properties of "temperature and molecular structure" important (heat capacity ratio may be determined by temperature and molecular structure, but simple molecular weight is not sufficient to determine it).
   BULLET::::- Graham's law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density at constant temperature. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.
  
  BULLET::::- Dalton's law of partial pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's law is as follows:
  
  or
   For most liquids, the volumetric heat capacity is narrower, for example octane at 1.64 MJ/K/m or ethanol at 1.9. This reflects the modest loss of degrees of freedom for particles in liquids as compared with solids.
  
  However, water has a very high volumetric heat capacity, at 4.18 MJ/K/m, and ammonia is also fairly high (3.3).
   In fluids, only the medium's compressibility and density are the important factors, since fluids do not transmit shear stresses. In heterogeneous fluids, such as a liquid filled with gas bubbles, the density of the liquid and the compressibility of the gas affect the speed of sound in an additive manner, as demonstrated in the hot chocolate effect.
   The amount of substance is also a convenient concept in thermodynamics. For example, the pressure of a certain quantity of a noble gas in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through the ideal gas law), not to its mass.
   Technically, a material is under a state of compression, at some specific point and along a specific direction formula_1, if the normal component of the stress vector across a surface with normal direction formula_1 is directed opposite to formula_1. If the stress vector itself is opposite to formula_1, the material is said to be under normal compression or pure compressive stress along formula_1. In a solid, the amount of compression generally depends on the direction formula_1, and the material may be under compression along some directions but under traction along others. If the stress vector is purely compressive and has the same magnitude for all directions, the material is said to be under isotropic or hydrostatic compression at that point. This is the only type of static compression that liquids and gases can bear
   The second physical factor which can lead to an LCST is compressibility effects, especially in polymer-solvent systems. For nonpolar systems such as polystyrene in cyclohexane, phase separation has been observed in sealed tubes (at high pressure) at temperatures approaching the liquid-vapor critical point of the solvent. At such temperatures the solvent expands much more rapidly than the polymer, whose segments are covalently linked. Mixing therefore requires contraction of the solvent for compatibility of the polymer, resulting in a loss of entropy.
  
  Section::::Theory.
   When a specimen of material is loaded in such a way that it extends it is said to be in "tension". On the other hand, if the material compresses and shortens it is said to be in "compression".
  
  On an atomic level, the molecules or atoms are forced apart when in tension whereas in compression they are forced together. Since atoms in solids always try to find an equilibrium position, and distance between other atoms, forces arise throughout the entire material which oppose both tension or compression. The phenomena prevailing on an atomic level are therefore similar.
   At constant pressure and temperature, the root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight. Gases with a lower molecular weight effuse more rapidly than gases with a higher molecular weight, so that the "number" of lighter molecules passing through the hole per unit time is greater. This is why a balloon filled with low molecular weight helium ("M" = 4) deflates faster than an equivalent balloon full of higher molecular weight oxygen ("M" = 32). However the total "mass" of the escaping molecules is directly proportional to the square root of the molecular weight and is less for lighter molecules.
   In contrast to other gas components, water content in air, or humidity, to a higher degree depends on vaporization and condensation from or into water, which, in turn, mainly depends on temperature. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. However, some of the water will condense until returning to almost the same humidity as before, giving the resulting total volume deviating from what the ideal gas law predicted. Conversely, decreasing temperature would also make some water condense, again making the final volume deviating from predicted by the ideal gas law.
  
presuppositions: Liquids can't be compressed. Liquids cannot be compressed as solids can.
corrections: Liquids like oil can be compressed. Liquids can be compressed.
raw_presuppositions: Liquids can't be compressed. Liquids cannot be compressed as solids can.
raw_corrections: Liquids like oil can be compressed. Liquids can be compressed.