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dos.3: Matchmaking certainly Stress, Temperatures, Volume, and you will Count

Early experts explored the fresh relationships among tension off a fuel (P) and its temperatures (T), frequency (V), and you may number (n) by carrying two of the five details constant (count and heat, eg), differing a 3rd (particularly stress), and you can computing the end result of your own transform to the 4th (in this instance, volume). The history of their discoveries brings several sophisticated examples of the newest scientific strategy.

The relationship between Tension and you may Frequency: Boyle’s Law

Once the stress for the a gasoline increases, the quantity of one’s energy decreases because gas particles is actually forced nearer along with her. On the other hand, since tension towards the a gas decreases, the brand new gasoline regularity increases because gas particles may now move further apart. Climate balloons get big while they go up from ambiance so you’re able to regions of down tension given that amount of the new gasoline has increased; that is, this new atmospheric energy exerts faster strain on the facial skin of the balloon, so that the indoor energy expands through to the internal and external challenges is actually equal.

2.3: Relationship one of Pressure, Temperatures, Volume, and Amount

The Irish chemist Robert Boyle (16271691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury, as shown in Figure \(\PageIndex<1>\). In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample. The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Data such as those from one of Boyles own experiments may be plotted in several ways (Figure \(\PageIndex<2>\)). A simple plot of \(V\) versus \(P\) gives a curve called a hyperbola and reveals an inverse relationship between pressure and volume: as the pressure is doubled, the volume decreases by a factor of two. This relationship between the two quantities is described as follows:

Figure \(\PageIndex<1>\): Boyles Experiment Using a J-Shaped Tube to Determine the Relationship between Gas Pressure and Volume. (a) Initially the gas is at a pressure of 1 atm = 760 mmHg (the mercury is at the same height in both the arm containing the sample and the arm open to the atmosphere); its volume is V. (b) If enough mercury is added to the right side to give a difference in height of 760 mmHg between the two arms, the pressure of the gas is 760 mmHg (atmospheric pressure) + 760 mmHg = 1520 mmHg and the volume is V/2. (c) If an additional 760 mmHg is added to the column on the right, the total pressure on the gas increases to 2280 mmHg, and the volume of the gas decreases to V/3.

where in actuality the ? symbol was read “is proportional so you can.” A plot off V in place of step 1/P is actually therefore a straight-line whoever hill is equal to the constant into the Formula 6.2.1 and Formula six.dos.3. Separating each party regarding Formula six.2.1 of the V unlike P gives a similar relationship anywhere between P and you may step 1/V. This new recenzja chatango numerical worth of the constant depends on the level of gas included in the try and on heat from which new experiments are carried out. Which matchmaking anywhere between tension and you may volume is known as Boyles legislation, following its discoverer, and certainly will feel stated as follows: On ongoing temperatures, the quantity off a predetermined amount of a petrol are inversely proportional in order to the stress.

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