Experiments show that most of bodies increase their Volume upon heating. The extent of expansion of various bodies is characterized by the temperature coefficient of expansion, or simply the coefficient of expansion. While considering solid which retain their shape during temperature variations, the distinction is made between (a) a change in their linear dimensions (viz. the dimensions in a certain direction), i.e. linear expansion, and (b) a change in the volume of a body, i.e. cubic expansion.
The coefficient of linear expansion is the quantity α equal to the fraction of the initial length by which a body taken at 0oC has elongated as a result of heating it by 1oC (or by 1 K):
α = (lt – lo)/lot
where lo is the initial length at 0oC and lt is the length at a temperature t. From this expansion, we can find
lt = lo(1 + αt)
The dimensions of α are K-1 (or oC-1).
The coefficient of cubic expansion is the quantity γ equal to the fraction of the initial volume by which the volume of a body taken at 0oC has increased upon heating it by 1oC (or by 1 K):
γ = (Vt– Vo)/Vot,
where Vois the volume of a body at 0oC and Vtis its volume at a temperature t. From this equation, we obtain
Vt= Vo(1 + gt)
The quantity γ has also the dimensions of K-1 (or oC-1).
The coefficient of cubic expansion is about three times larger than the coefficient of linear expansion:
γ = 3α
The coefficients of γ of cubic expansion for liquids are somewhat higher than for solid bodies, ranging between 10-3 and 10-4 K-1.
What obeys the general laws of thermal expansion only at a temperature above 4 oC. From 0 oC to 4 oC, water contracts rather than expands. At 4 oC, water occupies the smallest volume, i.e. it has the highest density. At the bottom of deep lakes, there is denser water in winter, which remains the temperature of 4 oC even after the upper layer has been frozen.
The lengths l1i = 100 m of iron wire and l1c = 100 m of copper wire are marked off at t1 = 20 oC. What is the difference in lengths of the wires at t2 = 60 oC? The coefficients of linear expansion for iron and copper are α1 = 1.2 ´ 10-5 K-1 and αc = 1.7 ´ 10-5 K-1.
The Gases such as hydrogen, oxygen and helium etc. which can not be liquified easily are called permanent gases. The gases whose molecules are point masses (mass without having volume) and do not attract each other are called ideal or perfect gases. Assuming permanent gases to be ideal, through experiment it has been observed that, these gases irrespective of their nature obey the following laws.
(a) Boyle’s Law
For a given mass of an Ideal Gas at constant temperature, the volume of a gas is inversely proportional to its pressure. i.e.
(b) Charle’s law
For a given mass of an ideal gas at constant Pressure, volume of a gas is directly proportional to its absolute temperature. i.e.
(c) Gay – Lussac’s Law
For a given mass of an ideal gas at constant volume, pressure of a gas is directly proportional to its absolute temperature
i.e. P ∝ T
(d) Avagadro’s Law
At the same temperature, pressure and volume all gases contain equal number of molecules. At STP or NTP (0oC and 1 atm i.e. 273 K and 1.01 × 105 N/m2).
1 mole of an ideal gas º NA ( = 6.02 × 1023) molecules of gas
=22.4 litre of the gas = M (molecular weight) gram of the gas
(e) Graham’s Law
At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density
(f) Ideal gas Equation
Combining first four laws (i.e. Boyle’s law, Charle’s Law, Gay – Lussac’s Law and Avagadro’s law) we get one single equation for an ideal gas, i.e.
(g) Dalton’s Law
The pressure exerted by a gaseous mixture is equal to the sum of partial pressure of each component present in the mixture.
i.e. P = P1 + P2 + ………… (10.2)
A vessel of volume 2 × 10-3 m3 contains 0.1 mol of hydrogen gas and 0.2 mol of helium. If the temperature of the mixture is 300 K, calculate the pressure due to component gases and the mixture. (R = 8.31 J/mol K)
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