Title: Gas
Content:  The symbol used to represent temperature in equations is T with SI units of kelvins. The speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a molecule (also known as the thermal energy). The methods of storing this energy are dictated by the degrees of freedom of the molecule itself (energy 
Title: Temperature
Content: is the root-mean-square speed. This direct proportionality between temperature and mean molecular kinetic energy is a special case of the equipartition theorem, and holds only in the classical limit of a perfect gas. It does not hold exactly for most substances. Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases. This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases. The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states:
Title: Gas laws
Content: where P is the pressure ; V is the volume ; N is the number of gas molecules ; k is the Boltzmann constant (1.381×10−23J·K−1 in SI units) ; T is the temperature (K) 1) If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas. ; 2) If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present. ; 3) If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume. 
Title: Temperature
Content:  A material on which a macroscopically defined temperature scale may be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature range that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. In contrast to real materials, the ideal gas does not liquefy or solidify, no matter how cold it is. Alternatively thinking, the ideal gas law, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of the constituent molecules.
Title: Charles's law
Content: V is the volume of the gas, ; T is the temperature of the gas (measured in kelvins), and ; k is a non-zero constant.  Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statemet of Charles's law is: When the pressure on a sample of a dry gas is held constant, the temperature and the volume will be in direct proportion. This relationship of direct proportion can be written as: where: This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as: The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.
Title: Volume (thermodynamics)
Content: p is the pressure ; V is the volume ; n is the amount of substance of gas (moles) ; R is the gas constant, 8.314 J·K−1mol−1 ; T is the absolute temperature The volume of gas increases proportionally to absolute temperature and decreases inversely proportionally to pressure, approximately according to the ideal gas law: where: To simplify, a volume of gas may be expressed as the volume it would have in standard conditions for temperature and pressure, which are 0 °C and 100 kPa.
Title: Gas laws
Content:  4) If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature. The Combined gas law or General Gas Equation is obtained by combining Boyle's Law, Charles's law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature for a fixed mass (quantity) of gas:    These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature. This law has the following important consequences:
Title: Thermodynamic temperature
Content:  velocity have precisely the same kinetic energy, and precisely the same temperature, as those with four times the mass but half the velocity. The extent to which the kinetic energy of translational motion in a statistically significant collection of atoms or molecules in a gas contributes to the pressure and volume of that gas is a proportional function of thermodynamic temperature as established by the Boltzmann constant (symbol: kB). The Boltzmann constant also relates the thermodynamic temperature of a gas to the mean kinetic energy of an individual particles’ translational motion as follows: is the mean kinetic energy for any individual particle, 
Title: Thermodynamic temperature
Content:  is what gives gases not only their temperature, but also their pressure and the vast majority of their volume. This relationship between the temperature, pressure, and volume of gases is established by the ideal gas law's formula pV = nRT and is embodied in the gas laws. Though the kinetic energy borne exclusively in the three translational degrees of freedom comprise the thermodynamic temperature of a substance, molecules, as can be seen in Fig. 3, can have other degrees of freedom, all of which fall under three categories: bond length, bond angle, and rotational. All three additional categories are not necessarily available 
Title: Heat capacity ratio
Content:  As temperature increases, higher-energy rotational and vibrational states become accessible to molecular gases, thus increasing the number of degrees of freedom and lowering γ . For a real gas, both CP and CV increase with increasing temperature, while continuing to differ from each other by a fixed constant (as above, CP = CV + nR ), which reflects the relatively constant PV difference in work done during expansion for constant pressure vs. constant volume conditions. Thus, the ratio of the two values, γ , decreases with increasing temperature. For more information on mechanisms for storing heat in gases, see the gas section of specific heat capacity. While at 273 K (0 °C), Monatomic gases such as the noble gases He, Ne, and Ar all have the same value of γ , that being 1.664.

Question: the temperature of gas is proportional to the?
Answer: volume.