ANSWERS: 6

According to Boyle’s law, the pressure exerted by a given quantity of gas increases as the volume of the gas decreases at a constant temperature. According to Charles’s law, at a constant pressure, the volume occupied by a given quantity of gas decreases as the temperature of the gas decreases. According to Avogadro’s principle, the volume occupied by a gas depends directly on the number of gas particles at a constant temperature and pressure. If all three of these laws are combined, the result is V= R*((nT)/P). R is the universal gas constant which is equal to 0.0821 L*atm/mol K (Kelvin). By multiplying both sides of this equation by P, the equation would become PV=nRT, the ideal gas law. Note: P=Pressure (atm), V=Volume (L), n=number of moles, and T= Temperature (Kelvin)). So, PV=nRT means Pressure * volume = numberber of moles * 0.0821 * Temperature. Without getting into too much detail, let's say that temperature is directly proportional to pressure and volume. When volume (the can) is constant and pressure decreases, the temperature also decreases. Look at it this way: PV=T For example (omitting the units should avoid further confusion), P= 10, V= 10, T= 100 10 * 10 = 100. Let's lower the pressure to 8. P= 8 V=10 (again, this is constant), T= 80. 8 * 10 = 80. The same works in reverse. When the can is a constant size, increasing the pressure increases the temperature. PV=T We'll start the with the same ammounts: P=10, V=10, T= 100 10 * 10 = 100 Let's raise the pressure to 120. P=120, V= 10, T= 1200 120 * 10 = 1200 This quick answer is simplified, but it should give you the general idea of what is going on.

No one has yet said why the gas laws are as they are? WHY does temperature decrease as pressure decreases? Temperature is a measure of heat energy per unit mass. When you let out some air, the pressure difference forces the air into motion  this motion energy comes from the heat energy of the air molecules in the can, so the temperature goes down.

I am not sure that PV=nRT applied in this manner, to an open system, is correct. One can not ignore that n, the number of moles, is also changing as gas is released from the canister. In the first explanation above, n was assumed constant.

That is a very nice answer from Quirkie and I believe it to be true. Let me restate. As mass is expelled, it acquires kinetic energy (KE=.5mv^2), mass in motion. Due to conservation of energy, the gas in the canister reduces its temperature (mean molecular energy) which was the potential energy source for expelling the gas. This is a conceptual explanation. Rather than the PV=nRT equation above used to describe this process we should use isentropic relations between temperatures and pressures in an ideal isentropic process. I think we can assume the canisters decompression as approximately isentropic. Then (T2/T1)=(P2/P1)^((gamma1)/gamma) where gamma= Cp/Cv (specific heat ratio at constant pressure Cp and constant volume Cv, this ratio is always greater than 1) Gamma = 1.4 for air. We can only use this equation if we assume the process to be isentropic, meaning that there is no heat addition dq=0 and there are no irreversible losses ds=0 (entropy does not increase). With P2 less than P1, P2/P1<1. For air (gamma1)/gamma < 1. Work it out, T2 will be less than T1. Someone correct me if I am wrong but another source for the change in temperature could be that required heat of sumlimation, (when a solid turns to gas). Because many of these pressurized canisters have a substantial amount of liquid. As this liquid sublimates it should cool just like our body sweat evaporating. If this is true, perhaps someone could give a conceptual explanation for why this happens.

Hmm.. to put it in simple way the pressure in the can is due to internal energy of the molecules of gas,now release the gas all of sudden, then gas will come out but it needs energy to come out,it will use its own energy, thjat means gas used its internal energy,since it lost its energy, its gets cold thus can in which it was kept becomes cold. (But it follows certain laws) In physics, the Joule–Thomson effect or Joule–Kelvin effect describes the increase or decrease in the temperature of a real gas when it is allowed to expand freely at constant enthalpy (which means that no heat is transferred to or from the gas, and no external work is extracted) As a gas expands, the average distance between molecules grows. Because of intermolecular attractive forces (Van der Waals force), expansion causes an increase in the potential energy of the gas. If no external work is extracted in the process (“free expansion”) and no heat is transferred, the total energy of the gas remains the same because of the conservation of energy. The increase in potential energy thus implies a decrease in kinetic energy and therefore in temperature.(cryogenic processes are designed on this basis (Remember Linde process)

I agree with chancemanthough I would like to think science isn't a democracy. Phase changes are always accompanied by a change in energy, e.g., heating water to a boil. In this case, the liquid (compressed gas) is going to gas phase. The energy used in the phase change is heat from ambient temperature. The feeling of coldness is energy in the form of heat from the surroundings being absorbed into the liquid, changing it to gas.
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