Choose the correct option for graphical representation of Boyle's law, which shows a graph of pressure vs. volume of a gas at different temperatures:
The Correct Option is D
Solution and Explanation
Boyle's Law states that for a given mass of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. Mathematically, it is expressed as:
PV = kwhere:
- P is the pressure of the gas,
- V is the volume of the gas, and
- k is a constant for a given amount of gas at a constant temperature.
The graphical representation of Boyle's Law is a curve that shows pressure vs. volume at constant temperature, also known as an isotherm. The curve is hyperbolic, depicting the inverse relationship between the pressure and volume.
Let's examine the given options:
1. Option 1 shows multiple curves with varying shapes.
2. Option 2 appears to be lines instead of curves, which does not represent Boyle's Law accurately.
3. Option 3 also shows a pattern inconsistent with the hyperbolic shape expected for Boyle's Law.
4. Option 4 displays a set of downward-sloping hyperbolic curves on a graph of Pressure vs. Volume, which matches the characteristics of Boyle's Law at different constant temperatures.
Hence, the correct graphical representation of Boyle's Law is shown in Option 4, where each curve represents an isotherm at a different temperature.
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Concepts Used:
Gas Laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
The five gas laws are:
- Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
- Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
- Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
- Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
- The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.