According to Charle's Law, which of the following is constant?
Understanding Charles's Law and Gas Relationships
Charles's Law is one of the fundamental gas laws that describes the relationship between the volume and temperature of an ideal gas. It states that for a fixed amount of gas at constant pressure, the volume occupied by the gas is directly proportional to its absolute temperature.
Mathematically, Charles's Law can be expressed as:
\(V \propto T\)
or
\(\frac{V}{T} = k\)
Where:
- \(V\) is the volume of the gas
- \(T\) is the absolute temperature of the gas (in Kelvin)
- \(k\) is a constant, which depends on the amount of gas and the pressure
According to Charles's Law, when the pressure and the amount of gas are kept constant, the ratio of the volume of the gas to its absolute temperature is constant. This means that if the volume of a gas increases, its temperature also increases proportionally, and vice versa, assuming the pressure remains the same.
Analyzing the Options
Let's look at the given options in the context of what remains constant according to Charles's Law:
- Option 1: PT - This represents the product of pressure and temperature. Charles's Law requires pressure (P) to be constant, but it relates Volume (V) and Temperature (T), not P and T directly in this product form being constant.
- Option 2: PV - This represents the product of pressure and volume. According to Boyle's Law, PV is constant at constant temperature for a fixed amount of gas. Charles's Law, however, deals with constant pressure and relates V and T.
- Option 3: \(\frac{V}{T}\) - This represents the ratio of volume to absolute temperature. According to Charles's Law, this ratio is constant for a fixed amount of gas at constant pressure.
- Option 4: \(\frac{P}{T}\) - This represents the ratio of pressure to absolute temperature. According to Gay-Lussac's Law (or Amontons's Law), this ratio is constant at constant volume for a fixed amount of gas. Charles's Law deals with constant pressure.
Based on the definition and mathematical formulation of Charles's Law, the quantity that remains constant is the ratio of the volume to the absolute temperature, \(\frac{V}{T}\), provided the amount of gas and pressure are held constant.
Revision Table: Comparing Gas Laws
It's helpful to compare Charles's Law with other common gas laws to understand their differences.
| Law | Relationship | Constant Conditions | Mathematical Form |
|---|---|---|---|
| Boyle's Law | Pressure and Volume | Temperature, Amount of Gas | \(PV = \text{constant}\) |
| Charles's Law | Volume and Temperature | Pressure, Amount of Gas | \(\frac{V}{T} = \text{constant}\) |
| Gay-Lussac's Law | Pressure and Temperature | Volume, Amount of Gas | \(\frac{P}{T} = \text{constant}\) |
| Avogadro's Law | Volume and Amount | Temperature, Pressure | \(\frac{V}{n} = \text{constant}\) |
| Ideal Gas Law (Combines above) | P, V, T, n | Gas Constant (R) | \(PV = nRT\) |
Additional Information about Charles's Law
- Absolute Temperature: It is crucial that temperature in Charles's Law calculations is always in the absolute scale, which is Kelvin (K). The relationship does not hold true for Celsius or Fahrenheit scales because they do not have a true zero point that corresponds to zero kinetic energy. \(0^\circ\text{C} = 273.15 \text{ K}\).
- Constant Pressure: The pressure exerted by the gas must remain unchanged throughout the process. This is often achieved by using a container with a movable piston.
- Fixed Amount of Gas: The number of moles (n) or mass of the gas must be constant. No gas is added or removed.
- Ideal Gas Behavior: Charles's Law, like other gas laws, is an idealization. Real gases approximate this behavior closely at relatively low pressures and high temperatures.
Important Questions from States of Matter
Which is correct statement ?
Which of the following statements is/are correct?
I. Mass vapor is obtained in the air by evaporation and transpiration.
II. Water circulation between the oceans and the water bodies is called the water cycle.
Which state of matter is characterized by a high-energy collection of ionized particles, where atoms have lost or gained electrons, making it electrically conductive, and is the most common state of matter in the universe?
A change of state directly from solid to gas without changing into liquid state is called
Henry’s law is not applicable if:
