Gases

Question 3.5: Explains the derivation of absolute zero from the original definition of Charles's law. Also give graphical explanation.

Answer: The quantitative definition of Charles's law may be given as follows. "At constant pressure, the volume of a given mass of a gas increases or decrease by 1/273 of original volume at 0 ^οC for every 10 ^οC rise or fall in temperature respectively".

Explanation: Suppose the original volume of the gas is 546 cm³ at 0 ^οC. For each 1 ^οC rise in temperature volume of the gas increase by 546 x1/273 = 2 cm³. When the temperature is raised by 273, the volume of the gas becomes doubled i.e 1092 cm³. On the other hand, if the temperature is lowered to -273 ^οC or more correctly -273.15 ^οC, the volume of the gas is reduced to zero. This temperature is called 0K or absolute zero. The scale on which -273.15 ^οC is taken as zero is called Kelvin scale or absolute scale. The temperature measured on this scale is called Kelvin temperature or absolute temperature.

Graphical Explanation of Kelvin zero: Another way of explaining Kelvin zero is to plot volume versus temperature as shown in below. The straight line is obtained. The straight line cuts the temperature axis at -273.15 ^οC. This is possible if the line is extrapolated into -273.15 ^οC. This is the lowest possible temperature. All gases liquefy before this temperature if reached. At this temperature the volume of a real gas ends.

Figure: A plot between volume and temperature

Question: What are scales of thermometry?

Answer: There are three scales of temperature measurement.
i. Centigrade scale: It measured temperature from 0 ^οC to 100^οC. The former is freezing point of water and the letter is its boiling point. The space between these two temperatures is divided into 100 equal pads and each pad is I ^οC.
ii. Fahrenheit scale: It measures temperature from 32^οF to 212 ^οF. The former is freezing point of water and the later is its boiling point. The space between these two temperatures is divided into 180 equal parts and each part is I ^οF. iii. Absolute or Kelvin scale: At this scale freezing point of water is 273 K and the boiling point of water is 373 K.

Question. Derive general gas equation from the relevant gas laws.

Answer. General gas equation is derived from gas laws as follows:

Continued

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