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As typically measured, one kcal/mol represents a temperature increase of one degree Celsius in one liter of water (with a mass of 1 kg) resulting from the reaction of one mole of reagents. In SI units, one kilocalorie per mole is equal to 4.184 kilojoules per mole (kJ/mol), which comes to approximately 6.9477 × 10 −21 joules per molecule, or ...
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: = = Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K ...
2 at constant volume is 20.6 J⋅K −1 ⋅mol −1 (at 15 °C, 1 atm), which is 2.49 R. [11] From the theoretical equation c V,m = 1 / 2 fR, one concludes that each molecule has f = 5 degrees of freedom. These turn out to be three degrees of the molecule's velocity vector, plus two degrees from its rotation about an axis through the ...
For gases, departure from 3 R per mole of atoms is generally due to two factors: (1) failure of the higher quantum-energy-spaced vibration modes in gas molecules to be excited at room temperature, and (2) loss of potential energy degree of freedom for small gas molecules, simply because most of their atoms are not bonded maximally in space to ...
For example, the heat capacity of water ice at the melting point is about 4.6R per mole of molecules, but only 1.5R per mole of atoms. The lower than 3 R number "per atom" (as is the case with diamond and beryllium) results from the “freezing out” of possible vibration modes for light atoms at suitably low temperatures, just as in many low ...
[1] [2] The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter of water by one degree Celsius (or one kelvin). [1] [3] The small calorie or gram calorie is defined as the amount of heat needed to cause the same increase in one milliliter of ...
In monatomic gases (like argon) at room temperature and constant volume, volumetric heat capacities are all very close to 0.5 kJ⋅K −1 ⋅m −3, which is the same as the theoretical value of 3 / 2 RT per kelvin per mole of gas molecules (where R is the gas constant and T is temperature). As noted, the much lower values for gas heat ...
The "grand calorie" (also "kilocalorie", "kilogram-calorie", or "food calorie"; "kcal" or "Cal") is 1000 cal, that is, exactly 4184 J. It was originally defined so that the heat capacity of 1 kg of water would be 1 kcal/°C. With these units of heat energy, the units of heat capacity are 1 cal/°C = 4.184 J/K ; 1 kcal/°C = 4184 J/K.