#### Gas Laws, Physics tutorial

Gas laws:

Four properties are utilized to explain the behavior of gases; that is: Pressure (P), Volume (V), Temperature (T), and Amount of gas in moles (n). When any two of the properties are kept constant, other two are then subjected to change to show how gas behaves. First two will be considered while temperature and number of moles of gas is kept constant.

Boyle's Law Boyle (1662) investigated relationship between pressure (P) and volume (V) of the given mass of gas when temperature (T) and number of moles (n) are kept constant. Boyle's law defines that: Pressure on the given mass of gas is inversely proportional to volume (V) provided its temperature is kept constant. Symbolically, this statement is written as:

P ∝  1/v

Hence P = K/V where, K is the constant of proportionality.

PV = K = Constant

Charles's Law:

Charles's law deals with behavior of the given mass of gas at constant pressure. Under this law, we would consider variation of volume (V) with temperature (T) when pressure (P) and the amount of the gas (n) are kept constant. Original Charles's define that: At constant pressure, volume of the given amount of gas increases by the constant fraction of volume at 0oC for each Celsius degree rise in temperature.

Mathematical expression for this can be written as: V ∝ T (at constant n and P)

The above statement brings out idea of volume coefficient, r, where r is stated as increase in volume of the unit volume of gas at 0oC for each degree Celsius rise in temperature when fixed mass of that gas is heated at constant pressure. Volume coefficient is known as volume expansivity. If Vo is volume of gas at 0oC and Vo is volume of gas at toC, then r is stated as:

r = ΔV/VoΔΘ

= (Vt - Vo)/Vo(t-0)

Therefore r = (Vt - Vo)/Vot

Therefore Vt = Vo + rVot

Vt = Vo(1 + rt).........................E.q.1

Vo stands for volume of gas at 0oC and not just original volume at any selected initial temperature. And that t is actual temperature utilizing Celsius scale and not for any selected temperature rise. Valve of r for most gases is(1/273). Now substituting value of r in Eq.1, we get

Vt = Vo[(273 + t)/273] ).........................E.q.2

But as you know from absolute scale,

(273 + t) = T# and that

273 = To.........................E.q.3

Then putting the values in Eq.3 into Eq. 2, we get

Vt = VoT/To On rearranging the terms, we get

Vt = K# i.e. Vt ∝ T

Therefore volume of the gas (V) is directly proportional to the absolute temperature (T). Equation Vt = KT is the deduction, or consequence of Charles's law. It is not law.

Pressure Law:

Pressure law defines that: For the given mass of the gas at constant volume, its pressure increases by the constant fraction of pressure at 0oC for every Celsius degree rise in temperature. Let us consider the fixed mass of gas of volume V1at t1oC and pressure P1. Assume gas is then heated to some temperature t2oC at which volume is zV1. Where z is the fraction. We can reduce this new volume zV1 to V1 at higher temperature by increasing pressure using Boyle's law.

P2V1 = P1 zV1 ∴ P2 = zP1 Therefore, when temperature is raised, volume can be maintained at V1by increasing pressure. That is, rise in temperature, that causes the increase in volume from V1 to zV1if pressure is kept at P1, also causes the increase in pressure from P1to zP1 if volume is kept constant at V1. If Boyle's law is not obeyed entirely then theoretical basis fails. Though, experiment have illustrated that when the fixed mass of gas is heated at constant volume, its pressure increase s by the constant fraction of pressure at 0oC for each degree Celsius rise in temperature.

The above statement hence states pressure coefficient β or pressure expansivity. Pressure coefficient β is stated as increase in pressure expressed as the fraction of pressure at 0oC for one Celsius degree rise in temperature when the fixed mass of that as is heated at constant volume. If Po is pressure of gas at 0oC and P, pressure at toC, then is defined as:

β = ΔP/Pot

Therefore β = (Pt - Po)/Pot

Therefore Pt - Po = βPot

Therefore Pt = Po(1 + βt)

Constant volume Gas Thermometer:

Temperature readings provided by the gas thermometer are almost independent of substance utilized in thermometer. One version is constant-volume gas thermometer. Physical change exploited in the device is the variation of pressure of the fixed volume of gas with temperature. When constant-volume gas thermometer was developed, it was calibrated by using ice and steam points of water. Flask was immersed in the ice bath, and mercury reservoir B was raised or lowered until top of the mercury in column A was at the zero point on the scale. Height h, difference between mercury levels in reservoir B and column A, signified the pressure in flask at 0°C. Flask was then immersed in water at steam point, and reservoir B was readjusted until top of mercury in column A was again at zero on scale; this made sure that gas's volume was same as it was when flask was in the ice bath (therefore, designation constant volume). This adjustment of reservoir B provided value for gas pressure at 100°C. Line connecting two points acts as calibration curve for unknown temperatures. If we wanted to estimate temperature of the substance, we would put gas flask in thermal contact with the substance and adjust the height of reservoir B until the top of the mercury column in A was at zero on the scale. Height of the mercury column would point to pressure of the gas.

Real Gases and Ideal Gases:

Gases, unlike solids and liquids have indefinite shape and indefinite volume. Consequently, they are subject to pressure changes, volume changes and temperature changes. Real gas behavior is really complex. The ideal gas has the properties which are given below:

An ideal gas is regarded as point mass. The point mass is the particle so small, it's mass is very almost zero. This signifies the ideal gas particle has virtually no volume.

Collisions between ideal Gases are elastic. This signifies that no attractive or repulsive forces are involved during collisions. Also, kinetic energy of gas molecules remains constant as these interparticle forces are lacking.

Ideal gases are gases which obey gas laws like Boyle law, Charles Law and Avogadro Law over all temperature and pressures. By combining Boyle's and Charles' laws, the equation can be deduced which provides overall relationship between pressure, temperature and volume of gas. This is called as combined Ideal Gas Equation. We can deduce equation as under. According to Boyle's law, for the given gas at constant temperature volume is inversely proportional to pressure of gas.

Real gases as opposed to the perfect or ideal gas show properties which can't be explained completely using ideal gas law. To known behavior of real gases, the following should be take into consideration:

• Compressibility effects;
• variable specific heat capacity;
• van der Waals forces;
• non-equilibrium thermodynamic effects;

Absolute zero:

Absolute zero is the lowest possible temperature where nothing could be colder and no heat energy remains in the substance.

Absolute zero is a point at which fundamental particles of nature have minimal vibrational motion, keeping only quantum mechanical, and zero - point energy-induced particle motion.

By international agreement, absolute zero is stated as precisely; 0 K on Kelvin scale, that is a thermodynamic (absolute) temperature scale; and -273.15 degrees Celsius on Celsius scale.

Absolute zero is also precisely equal to; 0 degrees R on Rankine scale (also a thermodynamic temperature scale); and -459.67 degrees F on Fahrenheit scale.

While scientists cannot fully attain the state of zero heat energy in the substance, they have made great advancements in getting temperatures ever closer to absolute zero (where matter shows odd quantum effects).

Absolute Temperature:

If you estimate temperature relative to absolute zero, temperature is the absolute temperature; absolute zero is 0.

Most widely utilized absolute temperature scale is Kelvin, symbolized with the capital K that uses Celsius-scaled degrees (there is another one, Rankine that is related to Fahrenheit scale). We write temperatures in kelvins without degree symbol; absolute zero is 0 K.

Universal gas Constant:

The gas constant is the physical constant that is featured in several fundamental equations in physical sciences, like ideal gas law and the Nernst equation.

It is equal to Boltzmann constant, but stated in units of energy (that is pressure-volume product) per temperature increment per mole (rather than energy per temperature increment per particle). Constant is also the combination of constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law.

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