Charle’s law explains the behavior of gases when heated. The law discusses the relationship between volume and temperature where pressure remains constant.
Mathematically, it can be written as V/ T = K.
The ratio between temperature and volume remains constant for the same amount of gas at the same pressure.
Quantitatively, it can be stated as the volume of a given mass of a gas increases or decreases by 1/273 of its original volume at 0 °C for every 1 °C rise or fall in temperature respectively, when pressure is kept constant.
Charle’s law provides experimental verifications.
- 1) Charle’s law
- 2) Mathematical Expression:
- 3) Experimental Verification of Charles’s Law
- 4) Derivation of Absolute Zero
- 5) Graphical Explanation
- 6) MCQs on Charle’s Law
- 7) Frequently Asked Questions (FAQs) about Charles’s Law:
- 8) 10 Problem/Solutions for Charle’s law
- 9) Wrap up
- 10) You may also like to learn:
Charle’s law
French scientist J. Charles in 1787 presented his law that describes how gases tend to expand when heated. The relationship between volume and temperature keeping the pressure constant was also studied.
The law mentions that:
“The volume of a given mass of a gas is directly proportional to the absolute temperature if the pressure is kept constant”.
Mathematical Expression:
When pressure P is constant, the volume V of a given mass of a gas is proportional to absolute temperature T. Mathematically, it is represented as:
Volume αtemperature; which can be represented as
V α T
V= kT or V/T= k
Where k is proportionality constant. If the temperature level of the gas is increased, its volume also increases. When the temperature is changed from T1 to T2, the volume changes from V1 to V2. The mathematical kind of Charles’ Law will be:
V1/T1= k and V2/T2= k
So, V1/T1= V2/T2
The ratio of volume to temperature stays constant for the same amount of gas at the very same pressure.
Experimental Verification of Charles’s Law
Let us consider a particular quantity of a gas confined in a cylinder fitted with a movable piston. The volume of the gas is V1 and its temperature is T1. When the gas in the cylinder is heated both volume and the temperature of the gas increase. The new values of volume and temperature are V2 andT2respectively. Experiment shows that
V1/T1= V2/T2
Hence, Charles’s law is verified.
Derivation of Absolute Zero
In order to obtain absolute zero of temperature, consider the following quantitative definition of Charles’s law.
“At constant pressure, the volume of the given mass of a gas increases or decreases by 1/273 of its original volume at 0°C for every 1°C rise or fall in temperature respectively”.
At 0 ° C, the volume of the gas taken is 546 cm3. It is twice 273cm3, and is being supposed for the benefit of understanding. At 273 ° C, the volume of the gas has actually doubled (1092 cm3) and it needs to become practically zero at -273 ° C. The basic formula to understand the volumes of the gas at different temperature levels is.
Vt = Vo (1+ t/273)
Where
- Vt = volume of gas at temperature T.
- Vo = Volume of gas at 0°C.
- t = Temperature on centigrade or Celsius scale.
If a gas is heated by 1°C, it expands by 1/273 of its original volume at 0°C. Considering that the initial volume is 546 cm3, so, for 1°C rise in temperature level, 2 cm3increase in volume will happen. 2cm3 is the 1/273 of 546 cm3. Similarly, for 100 °C rise in temperature level, a change of 200 cm3 will occur.
For example, the increase in temperature level from 10 °C to 100 °C, increases the volume from 566cm3 to 746cm3.
Using Charles’s law
The two sides of the equation are not equivalent. So, Charles’s law is not applicable when the temperature is measured on the Celsius scale.
For this reason, a new temperature scale has been established. It starts from 273 ° C (more precisely -273.16 ° C) which is called zero Kelvin or zero absolute.
Graphical Explanation
If we plot a chart in-between temperature on the x-axis and the volume of one mole of an ideal gas on the y-axis, we get a straight line that cuts the temperature level axis at-273.16 °C. This can be possible only if we theorize the graph up to -273.16 °C. This temperature is the lowest possible temperature, which would have been attained if the substance stays in the gaseous state.
In actuality, all the gases are converted into liquids above this temperature. Charles’s law is obeyed when the temperature is taken on the Kelvin scale. For instance, at 283 K (10 °C) the volume is 566 cm3, while at 373 K (100 °C) the volume is,746 cm3.
According to Charles’s law
The greater the mass of gas taken, the greater will be the slope of the straight line. The factor is that the greater the number of moles greater the volume occupied. All these straight lines when extrapolated meet at a single point of -273.16 ° C (0 Kelvin).
It appears that this temperature level of -273.16 ° C will be attained when the volume becomes absolutely zero. But for a genuine gas, the zero volume is not possible which shows that this temperature level can not be achieved for a real gas. This is how we recognize that-273.16 ° C must represent the coldest temperature level.
MCQs on Charle’s Law
- What does Charle’s law describe?
- A. The relationship between volume and pressure at constant temperature
- B. The relationship between volume and temperature at constant pressure
- C. The relationship between pressure and temperature at constant volume
- D. The relationship between mass and volume at constant temperature
- Answer: B. The relationship between volume and temperature at constant pressure
- What is the mathematical expression for Charle’s law?
- A. P/V = K
- B. V/T = K
- C. PV = nRT
- D. P/T = K
- Answer: B. V/T = K
- Who proposed Charle’s law and in which year?
- A. Robert Boyle, 1672
- B. J. Charles, 1787
- C. Avogadro, 1811
- D. Dalton, 1803
- Answer: B. J. Charles, 1787
- What is the condition for Charle’s law to hold true?
- A. Constant volume
- B. Constant pressure
- C. Constant temperature
- D. Constant mass
- Answer: C. Constant temperature
- How is Charle’s law quantitatively stated concerning the change in volume with temperature?
- A. The volume changes by 1/273 of its original volume for every 1°C change in temperature
- B. The volume changes by 273 times its original volume for every 1°C change in temperature
- C. The volume changes by 1/100 of its original volume for every 1°C change in temperature
- D. The volume remains constant with temperature changes
- Answer: A. The volume changes by 1/273 of its original volume for every 1°C change in temperature
- What does the ratio V/T represent in the mathematical expression of Charle’s law?
- A. Volume
- B. Temperature
- C. Proportionality constant
- D. Pressure
- Answer: C. Proportionality constant
- How is the mathematical expression of Charle’s law represented when the gas temperature increases?
- A. V1/T1 = V2/T2
- B. V1T1 = V2T2
- C. V1 + T1 = V2 + T2
- D. V1 – T1 = V2 – T2
- Answer: A. V1/T1 = V2/T2
- What is the purpose of the movable piston in the experimental verification of Charle’s law?
- A. To control pressure
- B. To control temperature
- C. To measure volume
- D. To create a vacuum
- Answer: C. To measure volume
- How is the absolute zero of temperature defined in Charles’s law?
- A. The temperature at which gases turn into liquids
- B. The temperature at which the volume becomes zero
- C. The temperature at which the gas volume is 1/273 of its original volume at 0°C
- D. The temperature at which the gas volume doubles
- Answer: C. The temperature at which the gas volume is 1/273 of its original volume at 0°C
- What is the formula for calculating the volume of gas at a given temperature using Charles’s law?
- A. Vt = Vo (1+ t/273)
- B. Vt = Vo + t/273
- C. Vt = Vo – t/273
- D. Vt = Vo * (1 – t/273)
- Answer: A. Vt = Vo (1+ t/273)
- According to Charles’s law, what happens to the volume of gas when heated by 1°C?
- A. It remains constant
- B. It decreases by 1/273 of its original volume
- C. It increases by 1/273 of its original volume
- D. It doubles
- Answer: C. It increases by 1/273 of its original volume
- Why is a new temperature scale, zero Kelvin or zero absolute, established in Charles’s law?
- A. To simplify calculations
- B. To ensure gases remain in the gaseous state
- C. To avoid negative temperature values
- D. To reach the coldest temperature level
- Answer: B. To ensure gases remain in the gaseous state
- In the graphical explanation of Charles’s law, at what temperature does the straight line cut the temperature level axis?
- A. -100°C
- B. -273.16°C
- C. 0°C
- D. 100°C
- Answer: B. -273.16°C
- What does the slope of the straight line in the graphical explanation of Charles’s law represent?
- A. Volume
- B. Temperature
- C. Mass of the gas
- D. Proportionality constant
- Answer: D. Proportionality constant
- According to Charles’s law, at what temperature does it appear that the volume becomes absolutely zero?
- A. 0 Kelvin
- B. -273.16°C
- C. 100°C
- D. 273°C
- Answer: A. 0 Kelvin
- What is the significance of the ratio V/T in Charle’s law?
- A. It represents the volume of the gas
- B. It represents the temperature of the gas
- C. It represents the proportionality constant
- D. It remains constant for the same gas at the same pressure
- Answer: D. It remains constant for the same gas at the same pressure
- How does Charles’s law define the behavior of gases when heated?
- A. The volume decreases with temperature
- B. The volume increases with temperature
- C. The pressure increases with temperature
- D. The pressure decreases with temperature
- Answer: B. The volume increases with temperature
- What does the absolute zero represent in Charles’s law?
- A. The lowest possible temperature for any substance
- B. The temperature at which gases turn into solids
- C. The temperature at which the gas volume is zero
- D. The temperature at which the gas pressure is zero
- Answer: A. The lowest possible temperature for any substance
- How does Charles’s law behave when the temperature is measured on the Kelvin scale?
- A. It is not applicable
- B. It follows a linear relationship
- C. It results in a curved graph
- D. It shows no change in volume with temperature
- Answer: B. It follows a linear relationship
- In the graphical explanation of Charles’s law, why does the straight line cut the temperature level axis at -273.16 °C?
- A. It represents the boiling point of the gas
- B. It indicates the starting point of the graph
- C. It signifies the coldest temperature level
- D. It corresponds to the freezing point of the gas
- Answer: C. It signifies the coldest temperature level
Frequently Asked Questions (FAQs) about Charles’s Law:
- What is Charles’s Law?
- Charles’s Law describes the relationship between the volume and temperature of a gas when pressure is kept constant.
- How is Charles’s Law mathematically expressed?
- Mathematically, Charles’s Law is expressed as V/T = K, where V is the volume, T is the temperature, and K is a constant.
- What does the ratio V/T represent in Charles’s Law?
- The ratio V/T represents the constant relationship between volume and temperature when pressure is held constant.
- Who proposed Charles’s Law, and when?
- Charles’s Law was proposed by French scientist J. Charles in the year 1787.
- What is the quantitative statement of Charles’s Law concerning volume and temperature changes?
- Quantitatively, the law states that the volume of a given mass of gas changes by 1/273 of its original volume at 0 °C for every 1 °C rise or fall in temperature, when pressure is kept constant.
- How is the experimental verification of Charles’s Law conducted?
- In an experimental setup, a specific quantity of gas is confined in a cylinder fitted with a movable piston. The volume and temperature changes are observed as the gas is heated, and the verification is done through the equation V1/T1 = V2/T2.
- What is the derivation of absolute zero in Charles’s Law?
- Absolute zero is derived based on the quantitative definition of Charles’s Law, stating that at constant pressure, the volume of a gas changes by 1/273 of its original volume at 0°C for every 1°C rise or fall in temperature.
- Why is a new temperature scale, zero Kelvin, introduced in Charles’s Law?
- The new temperature scale, zero Kelvin, is introduced to ensure that gases remain in the gaseous state, as the scale starts from -273.16 °C.
- How does Charles’s Law behave when the temperature is measured on the Celsius scale?
- Charles’s Law is not applicable when the temperature is measured on the Celsius scale due to the non-equivalence of the two sides of the equation.
- What is the graphical explanation of Charles’s Law?
- When a chart is plotted with temperature on the x-axis and the volume of an ideal gas on the y-axis, a straight line is obtained. This line intersects the temperature level axis at -273.16 °C, representing the lowest possible temperature.
- What does the slope of the straight line in the graphical explanation represent?
- The slope of the straight line in the graphical explanation represents the proportionality constant in Charles’s Law.
- At what temperature level does it appear that the volume becomes absolutely zero in Charles’s Law?
- It appears that the volume becomes absolutely zero at the temperature level of -273.16 °C, which is recognized as the coldest temperature level.
- Why is zero Kelvin considered as absolute zero in Charles’s Law?
- Zero Kelvin is considered as absolute zero because it represents the point where the volume becomes theoretically zero for a real gas.
- How does the volume of gas change with temperature according to Charles’s Law?
- According to Charles’s Law, as the temperature increases, the volume of the gas also increases proportionally, and vice versa.
- Is Charles’s Law applicable to all gases?
- Charles’s Law is generally applicable to ideal gases under the assumption of constant pressure and a fixed amount of gas. Real gases may deviate under certain conditions.
10 Problem/Solutions for Charle’s law
- Problem 1:
- A gas occupies a volume of 500 mL at 27°C. If the temperature is increased to 77°C while keeping the pressure constant, what will be the new volume?
- Solution 1:
- Initial temperature (T1) = 27°C
- Final temperature (T2) = 77°C
- Initial volume (V1) = 500 mL
- Using Charles’s Law (V1/T1 = V2/T2), calculate the new volume (V2).
- Problem 2:
- A sample of gas has a volume of 2.0 L at 0°C. If the temperature is decreased to -50°C at constant pressure, what will be the final volume?
- Solution 2:
- Initial temperature (T1) = 0°C
- Final temperature (T2) = -50°C
- Initial volume (V1) = 2.0 L
- Use Charles’s Law to find the final volume (V2) after the temperature change.
- Problem 3:
- A certain gas occupies 300 mL at 25°C. If the volume is reduced to 200 mL while maintaining constant pressure, what is the new temperature?
- Solution 3:
- Initial temperature (T1) = 25°C
- Final volume (V2) = 200 mL
- Initial volume (V1) = 300 mL
- Apply Charles’s Law to find the new temperature (T2).
- Problem 4:
- A gas is initially at a temperature of 100°C, and its volume is 1.5 L. If the volume is increased to 2.0 L at constant pressure, what is the new temperature?
- Solution 4:
- Initial temperature (T1) = 100°C
- Final volume (V2) = 2.0 L
- Initial volume (V1) = 1.5 L
- Use Charles’s Law to determine the new temperature (T2).
- Problem 5:
- A gas has a volume of 800 mL at -10°C. If the temperature is raised to 30°C, calculate the final volume assuming constant pressure.
- Solution 5:
- Initial temperature (T1) = -10°C
- Final temperature (T2) = 30°C
- Initial volume (V1) = 800 mL
- Apply Charles’s Law to find the final volume (V2).
- Problem 6:
- A gas occupies 2.5 L at 20°C. What will be its volume at 50°C, keeping the pressure constant?
- Solution 6:
- Initial temperature (T1) = 20°C
- Final temperature (T2) = 50°C
- Initial volume (V1) = 2.5 L
- Use Charles’s Law to calculate the new volume (V2).
- Problem 7:
- A gas has a volume of 1.0 L at 25°C. If the volume is doubled while maintaining constant pressure, what will be the new temperature?
- Solution 7:
- Initial temperature (T1) = 25°C
- Final volume (V2) = 2.0 L
- Initial volume (V1) = 1.0 L
- Determine the new temperature (T2) using Charles’s Law.
- Problem 8:
- A sample of gas occupies 400 mL at 15°C. If the temperature is lowered to -10°C, what will be the final volume?
- Solution 8:
- Initial temperature (T1) = 15°C
- Final temperature (T2) = -10°C
- Initial volume (V1) = 400 mL
- Apply Charles’s Law to find the final volume (V2).
- Problem 9:
- A gas expands from 2.0 L to 3.5 L as it is heated from 50°C to 80°C. Determine the constant pressure during this process.
- Solution 9:
- Initial temperature (T1) = 50°C
- Final temperature (T2) = 80°C
- Initial volume (V1) = 2.0 L
- Final volume (V2) = 3.5 L
- Use Charles’s Law to calculate the constant pressure.
- Problem 10:
- A gas initially occupies 300 mL at 30°C. If the temperature is raised to 60°C, find the final volume under constant pressure conditions.
- Solution 10:
- Initial temperature (T1) = 30°C
- Final temperature (T2) = 60°C
- Initial volume (V1) = 300 mL
- Determine the final volume (V2) using Charles’s Law.
Wrap up
This tutorial dives into Charles’s Law, which explains the relationship between the volume and temperature of gases at constant pressure. Here’s a brief overview of the key components covered in the tutorial:
- Abstract:
- Charles’s law explores how gases behave when heated, emphasizing the interplay between volume and temperature under constant pressure conditions.
- Mathematically, the law is expressed as V/T = K, where the ratio of temperature to volume remains constant for a given amount of gas at a specific pressure.
- Charle’s Law:
- French scientist J. Charles introduced this law in 1787, revealing how gases expand when subjected to heat.
- The law asserts that the volume of a gas is directly proportional to its absolute temperature when pressure is kept constant.
- Mathematical Expression:
- Under constant pressure (P), the relationship between volume (V) and absolute temperature (T) is represented as V α T.
- Mathematically, V = kT or V/T = k, where k is the proportionality constant.
- Experimental Verification:
- Experimental setups involving a gas confined in a cylinder validate Charles’s law.
- The law is affirmed through experiments demonstrating V1/T1 = V2/T2 when the volume and temperature change.
- Derivation of Absolute Zero:
- A quantitative definition of Charles’s law at constant pressure reveals that a gas’s volume changes by 1/273 of its original volume at 0°C for every 1°C rise or fall.
- The derivation leads to the concept of absolute zero, theoretically reached at -273.16°C.
- Graphical Explanation:
- Graphical representations, typically plotted on the Kelvin scale, illustrate Charles’s law as a straight line intersecting the temperature axis at -273.16°C.
- The graphical extrapolation suggests that -273.16°C represents the coldest temperature, where volume theoretically becomes zero.
This tutorial provides a comprehensive understanding of Charles’s Law, from its mathematical representation to experimental validations and the intriguing concept of absolute zero. Further explorations include graphical insights into gas behavior at extreme temperatures.