Gas Law and Kinetic Theory
Pressure is defined as perpendicular force per unit area. Mathematically P=F/A. It's a scalar, and has unit Nm^{-2} or Pascal (Pa), others including atm, mmHg or psi.
The pressure due to gas in a container is unique, and gas under higher pressure is pushed into region of lower pressure (since F=A*ΔP). Pressure can be measured by a Bourdon gauge.
Atmospheric pressure is the pressure due to the atmospheric environment (gas). It's about 101kPa (1atm)
Gas law – concerning P (pressure), V (volume), T (temperature), n (mass/amount of gas)
Note that T concerned is the absolute temperature, which implies the Kelvin scale. If a variable is directly proportional to absolute temperature, then it varies linearly with the temperature in Celsius scale.
1) Boyle's law: P inversely proportional to V under fixed n, T. Mathematically P_{1}V_{1}=P_{2}V_{2}.
2) Pressure law: P directly proportional to T under fixed n, V, Mathematically P_{1}/T_{1}=P_{2}/T_{2}.
3) Charles' law: V directly proportional to T under fixed n, P, Mathematically V_{1}/T_{1}=V_{2}/T_{2}.
4) General gas law : P_{1}V_{1}/T_{1}=P_{2}V_{2}/T_{2}. The gas is an ideal gas if it obeys this law for all temperature. Under room conditions, O, He, Ne behaves almost like an ideal gas. Gas behaves like ideal under very high T and very low P.
5) Ideal gas law: PV=nRT, where n is number of moles of the gas, and R=8.31Jmol^{-1}K^{-1} which is known as universal gas constant. There are different forms related to this law, such as PV=NkT, where N is number of molecules and k=R/N_{A}, where N_{A} is the Avogadro's number, 6.02*10^{23} mol^{-1}, and k=1.38*10^{-21}JK^{-1}.
Kinetic theory
Properties related to kinetic theory:
- Temperature of gas is the average KE due to random motion of the gas molecules.
- Volume of gas spreads freely throughout the container.
- Gas pressure is caused by collision of gas on the walls of container.
- Particles moves in zigzag paths (Brownian motion), since they always collide and change direction.
Kinetic theory model
- Boyle's law: weight added to piston (P↑), T unchanged, speed of molecules unchanged, it collides with the wall more frequently, exerting larger force, balancing weight of piston.
- Pressure law: Voltage supply increase (T↑), speed of molecules↑, it hits the walls more vigorously and frequently, exerting a larger force on the piston. In order to maintain the same volume (height of piston), a weight is added to balance the force exerted by the gas.
- Charles' law: Voltage supply increase (T↑), speed of molecules↑, it hits the walls more vigorously and frequently, exerting a larger force on the piston. P unchanged, therefore the weight of piston unchanged, then the piston moves upward to reduce frequency of collision, and reduce force exerted by the gas and balance the force.
Remaining part: Kinetic theory on ideal gas; internal energy.
doc. version of econ notes will be released soon.
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