P V = constant
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.
C- When tested in a local garage at 10 °C a motor tyre is found to have a pressure of 1.2 N / cm² . Assuming the volume of the air inside remains constant, what would you expect the pressure to become after the tyre has been allowed to stand in the sun so that the temperature rises to 37 °C ? ( Atmospheric pressure = 1.0 N / cm² .
In this problem it must be understood that 1.2 N / cm² is the excess pressure above atmospheric pressure and hence the absolute pressure inside the tyre is ( 1.2 + 1.0 ) = 2.2 N / cm².
Applying the pressure law
P / T = constant
or P2 / T2 = P1 / T1
We have,
T2 = 273 + 37 = 310 K
P1 = 1.2 + 1.0 = 2.2 N / cm²
Substituting in the equation,
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.
When the bulb is at any other temperature we measure the pressure and ascertain the gas temperature by reference to the graph.
Now, if the gas in the tube were perfect then the result obtained would agree with the Kelvin scale which is independent of the properties of any particular substance.
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 ).
In practice, therefore, such instruments as the platinum resistance thermometer, thermo-couples and so on are standardized by the fixed points so obtained and used to measure temperature over a wide range where mercury thermometers are unsuitable.
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