Combining the three laws of an ideal gas into one
Summarizing the gas laws dealt with, in our previous posts, we have
since, if T is constant, then PV = constent
or if P is constant, then V / T = constent
or if V is constant, then P / T = constant
It follows that P V / T = constant. includes all three gas laws.
Now, with the solved problems
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| Solved problems |
A-125 cm³ of gas are collected at 15 °C and 755 mm of mercury pressure. Calculate the volume of this gas at s.t.p.( standard temperature and pressure).
P / T = constant
Initial values
P1 = 755 mmHg
V1 = 125 cm³
T1 = ( 273 + 15 ) = 288 K.
Required values
P2 = 760 mmHg
V2 = ?
T2 = ( 273 + 0 ) = 273 K.
P2 V2/ T2 = P1 V1 / T1
or V2 = V1 × P1 / P2 × T2 / T1
hence, substituting numerical values, we obtain
volume of gas at s.t.p. = V2 = 125 × 755 / 760 × 273/288
= 118 cm³.
Assuming the temperature remains constant, Boyle’s law may be applied. i.e.,
or P1 V1 = P2 V2
Let h = depth, n m, of water-level in tube below surface, then
P2 = ( 10.4 + h ) in m of water
V2 = ( 0.8 × A ) in m³
where A = area of cross-section of tube in m² .
P1 = 10.4 in m of water
V1 = 1 × A in m³
Substituting in the above equation
( 10.4 + h ) ( 0.8 A ) = 10.4 × 1 × A
10.4 + h = 10.4 / 0.8 = 13
therefore h = 2.6 m
Hence top of tube is 2.6 – 0.8 = 1.8 m below surface.
Applying the pressure law
or P2 / T2 = P1 / T1
T2 = 273 + 37 = 310 K
P1 = 1.2 + 1.0 = 2.2 N / cm²
P2 / 310 = 2.2 / 283
whence P2 = 2.2 × 310 / 283 = 2.4 N / cm²
Therefore, new pressure as given by pressure gauge
= 2.4 – 1.0 = 1.4 N / cm².
Jolly’s constant volume apparatus as a thermometer in its own right
In the experiment with Jolly’s apparatus to measure the presuure coefficient of expansion of air we used a mercury thermometer to measure temperature.
Without using a mercury thermometer, we could calibrate the apparatus as a gas thermometer itself, simply by measuring the gas pressure first with the bulb in pure melting ice and then in steam. The Celsius scale of this thermometer is obtained by dividing the fundamental pressure interval into 100 equal parts, remembering that a suitable correction must be made if the steam is not at the standard pressure of 760 mmHg.
The most convenient way of representing the scale is to plot these two pressure values on a graph of pressure against temperature and to join them by a straight line.
Unfortunatly, no real gas is perfect but the one which comes most closely to this requirement is hydrogen.
An improved form of Jolly’s apparatus is called the standard gas thermometer. This thermometer needs laborious corrections and is far too difficult and cumbersome for ordinary day-to-day use. When very high temperatures are to be measured it is filled with nitrogen and is employed only for the purpose of obtaining accurate values for a number of other fixed points both above 100 °C and below 0 °C, e.g., the freezing-point of gold ( 1063 °C ) and the boiling-point of oxygen ( – 193 °C ).
P.s. This article is available in pdf format. The page is named download pdf.