State the laws which are represented by the following graphs
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Answer:
Boyle's law and Charles law easy aur answer
Answer: In 1787, the French scientist Jacques Charles discovered that volume of a gas varies when we change its temperature, keeping the pressure constant. Later, in 1802, Joseph Gay-Lussac modified the concept given by Charles and generalized it as Charles’s law. Gases obey Charles law at a very high temperature and low pressure.
It can be stated as:
“The volume of a fixed mass of a gas decreases on cooling it and increases by increasing the temperature. For one degree rise in temperature, the volume of the gas increases by 1/273 of its original volume at 0˚C. Let volume of the gas at 0˚C and t˚C be Vo and Vt respectively”.
Then, Vt = Vo+t x Vo/273.15 ……….. (i)
Vt = Vo(1+t/273.15) ……….. (ii)
Vt = Vo(273.15+t/273.15) ………… (iii)
We will now assign a new scale for temperature where the temperature in Celsius is given as t = T -273.15 and 0˚C can be given as To = 273.15. This new scale of temperature (T) is known as the Kelvin temperature scale or Absolute temperature scale. Degree sign is not written when a temperature is written in Kelvin scale. It is also known as the thermodynamic scale of temperature and it is commonly used in all scientific purposes. Thus, when we need to write temperature in Kelvin scale we add 273 to the temperature in Celsius.
Let us assume Tt = 273.15 + t
To = 273.15
Then equation (iii) can be written as
Vt = Vo(Tt/To)
Or, (Vt/Vo) = (Tt/To)
In general, we can write it as
(V2/V1) = (T2/T1)
Or, (V1/T1) = (V2/T2)
⇒V/T = constant = k2.
Hence, V =k2T..
The value of k2 depends on the pressure of the gas, its amount and also on the unit of volume V.
Volume and Pressure: Boyle’s Law
If we partially fill an airtight syringe with air, the syringe contains a specific amount of air at constant temperature, say 25 °C. If we slowly push in the plunger while keeping temperature constant, the gas in the syringe is compressed into a smaller volume and its pressure increases; if we pull out the plunger, the volume increases and the pressure decreases. This example of the effect of volume on the pressure of a given amount of a confined gas is true in general. Decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure. In fact, if the volume increases by a certain factor, the pressure decreases by the same factor, and vice versa. Volume-pressure data for an air sample at room temperature are graphed in Figure 5.
Unlike the P–T and V–T relationships, pressure and volume are not directly proportional to each other. Instead, P and V exhibit inverse proportionality: Increasing the pressure results in a decrease of the volume of the gas. Mathematically this can be written: with k being a constant. Graphically, this relationship is shown by the straight line that results when plotting the inverse of the pressure
(
1
P
)
versus the volume (V), or the inverse of volume
(
1
V
)
versus the pressure (V). Graphs with curved lines are difficult to read accurately at low or high values of the variables, and they are more difficult to use in fitting theoretical equations and parameters to experimental data. For those reasons, scientists often try to find a way to “linearize” their data. If we plot P versus V, we obtain a hyperbola (see Figure 6).
The relationship between the volume and pressure of a given amount of gas at constant temperature was first published by the English natural philosopher Robert Boyle over 300 years ago. It is summarized in the statement now known as Boyle’s law: The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured.
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