7.8.2 Variation of Volume and Pressure

We have seen how the expansion of liquids can be used to measure temperature. But liquids are not the only substances whose properties change with temperature. Gases also respond to temperature changes, and their response is even more dramatic. When a gas is heated, both its volume and its pressure can change in highly predictable ways. These variations are used in gas thermometers, which are among the most accurate temperature-measuring devices ever invented. Understanding how the volume and pressure of a gas vary with temperature is essential for understanding gas thermometers and the behavior of gases in general.

Definition

Variation of Volume and Pressure refers to the changes in the volume and pressure of a gas when its temperature changes. These changes are governed by the gas laws:

1. Charles's Law: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. V ∝ T (at constant P) 2. Gay-Lussac's Law: At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature. P ∝ T (at constant V)

Main Idea

The main idea is that the volume and pressure of a gas are directly proportional to its absolute temperature (when the other variable is held constant). This means that if you heat a gas, it will either expand (if the pressure is constant) or its pressure will increase (if the volume is constant). These predictable relationships are used in gas thermometers to measure temperature with high accuracy. The two main types of gas thermometers are the constant-pressure gas thermometer (which uses volume change) and the constant-volume gas thermometer (which uses pressure change).

Core Concept

Gas Thermometers The text states: "When a gas is heated, its volume as well as pressure may change. These variations in volume and pressure are used in gas thermometers to measure temperature. There are two types of gas thermometers, constant pressure gas thermometer and constant volume gas thermometer."

1. Constant-Volume Gas Thermometer The text states: "A constant volume gas thermometer, as shown in figure 7.9 (b) uses the principle that the pressure of a gas is directly proportional to the temperature, while the volume of the gas is kept constant (Gay-Lussac's law). We touch the thermometer bulb with the body whose temperature is to be measured. When the temperature of the thermometer bulb increases, the K.E. of gas particles increases. They collide with each other and the walls of the container more vigorously. This causes an increase in pressure. This variation in pressure is used to measure temperature."

• Principle: Gay-Lussac's Law (P ∝ T at constant V).
• Measurement: The pressure of the gas is measured and used to determine the temperature.
• Design: A gas is confined in a bulb of constant volume. A pressure gauge measures the pressure.
• Advantage: Very accurate; used as a primary standard for temperature measurement.

2. Constant-Pressure Gas Thermometer The text states: "A constant-pressure gas thermometer uses the principle that the volume of a gas is directly proportional to the temperature, while the pressure of the gas is kept constant (Charles's law). In this thermometer, the gas in its bulb expands and pushes a piston according to the increase in volume of the gas. This change in volume of the gas is used to measure its temperature."

• Principle: Charles's Law (V ∝ T at constant P).
• Measurement: The volume of the gas is measured and used to determine the temperature.
• Design: A gas is confined in a bulb, and the pressure is kept constant by allowing the volume to change (e.g., using a movable piston).
• Advantage: Also very accurate; suitable for a wide range of temperatures.

Detailed Explanation

Gas thermometers are among the most accurate temperature-measuring devices because the behavior of gases is well understood and described by simple laws.

• P is the pressure.
• V is the volume.
• n is the number of moles of gas.
• R is the universal gas constant (8.314 \frac{J}{mol·K}).
• T is the absolute temperature (in Kelvin).

• Constant Volume (Gay-Lussac's Law): If V and n are constant, then P ∝ T.
• Constant Pressure (Charles's Law): If P and n are constant, then V ∝ T.

The Constant-Volume Gas Thermometer This is the most common type of gas thermometer and is often used as a primary standard. A fixed mass of gas is confined in a bulb of constant volume. The pressure of the gas is measured using a manometer or a pressure gauge. Since P ∝ T (at constant V), the temperature can be determined from the pressure.

• Very high accuracy.
• Wide temperature range.
• Used as a primary standard (does not require calibration against another thermometer).

• Complex and bulky.
• Requires careful measurement of pressure and volume.
• Slow response time.

The Constant-Pressure Gas Thermometer In this type, the gas is allowed to expand or contract while the pressure is kept constant. The volume of the gas is measured, and since V ∝ T (at constant P), the temperature can be determined.

• Also very accurate.
• Can be used over a wide temperature range.

• Requires a mechanism to maintain constant pressure (e.g., a movable piston).
• More complex than liquid thermometers.

Why Use Gas Thermometers? Gas thermometers are used for calibration and for measuring temperatures where high accuracy is required. They are also used to establish the International Temperature Scale (ITS), which defines the standard temperatures used for calibration.

Intermediate Level

In physics, the variation of volume and pressure of a gas with temperature is described by the gas laws. For a fixed mass of gas:

• Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its absolute temperature: P ∝ T (or PT = constant).
• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its absolute temperature: V ∝ T (or VT = constant).

These laws are used in gas thermometers. The constant-volume gas thermometer uses the pressure of a gas at constant volume to measure temperature. It is a primary thermometer because it relies on fundamental physical laws and does not need calibration against another thermometer. It is the most accurate type of thermometer and is used to establish the International Temperature Scale.

The constant-pressure gas thermometer uses the volume of a gas at constant pressure to measure temperature. It is also very accurate but is more complex to operate.

Gas thermometers have some disadvantages: they are bulky, slow to respond, and require careful measurement. However, their accuracy makes them invaluable for calibration and for defining the standard temperature scale.

Important Points

• - Gas Thermometers: Use the variation of volume or pressure of a gas with temperature.
• - Constant-Volume Gas Thermometer: Uses P ∝ T (Gay-Lussac's Law). Measures pressure to determine temperature.
• - Constant-Pressure Gas Thermometer: Uses V ∝ T (Charles's Law). Measures volume to determine temperature.
• - Accuracy: Gas thermometers are among the most accurate.
• - Primary Standard: The constant-volume gas thermometer is used as a primary standard.
• - Applications: Calibration, defining the temperature scale.

Remember

• - Gas Thermometers: Volume or pressure change with temperature.
• - Constant-Volume: P ∝ T (Gay-Lussac's Law).
• - Constant-Pressure: V ∝ T (Charles's Law).
• - Accuracy: Very high (primary standard).
• - Ideal Gas Law: PV = nRT.

Common Mistakes

• - Confusing the two gas laws: Remember that Gay-Lussac's Law relates pressure and temperature at constant volume, while Charles's Law relates volume and temperature at constant pressure.
• - Forgetting to use absolute temperature (Kelvin): Gas laws apply only when temperature is in Kelvin. You must convert from Celsius to Kelvin by adding 273.15.
• - Thinking gas thermometers are simple: Gas thermometers are complex and bulky, requiring careful measurement of pressure and volume.

Quick Revision

Gas thermometers use the variation of volume or pressure of a gas with temperature to measure temperature. There are two types: the constant-volume gas thermometer (which uses Gay-Lussac's law, P ∝ T) and the constant-pressure gas thermometer (which uses Charles's law, V ∝ T). These thermometers are among the most accurate and are used as primary standards for temperature measurement. They require the use of absolute temperature (Kelvin).

60-Second Revision

• Constant-Volume: P ∝ T (Gay-Lussac's Law).
• Constant-Pressure: V ∝ T (Charles's Law).
• Accuracy: Very high (primary standard).
• Use Kelvin: T(K) = T(^°C) + 273.15.
• Ideal Gas Law: PV = nRT.

Frequently Asked Questions (FAQs)

Q1. What is a gas thermometer? Answer: A gas thermometer is a device that measures temperature by measuring the change in volume or pressure of a gas. It uses the gas laws (Charles's Law and Gay-Lussac's Law) to relate the gas's properties to temperature.

Q2. What is the difference between a constant-volume and a constant-pressure gas thermometer? Answer: A constant-volume gas thermometer keeps the volume constant and measures the pressure change with temperature (Gay-Lussac's Law). A constant-pressure gas thermometer keeps the pressure constant and measures the volume change with temperature (Charles's Law).

Q3. Why are gas thermometers so accurate? Answer: Gas thermometers are accurate because they rely on fundamental physical laws (the gas laws) that are well understood and can be precisely described. The constant-volume gas thermometer is used as a primary standard because it does not require calibration against another thermometer.

Q4. What is Gay-Lussac's Law? Answer: Gay-Lussac's Law states that at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature: P ∝ T.

• Q5. What is Charles's Law?
• Answer: Charles's Law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: V ∝ T.

Q6. Why must absolute temperature (Kelvin) be used in gas laws? Answer: Because the gas laws are derived from the ideal gas law, which relates pressure, volume, and absolute temperature. If Celsius is used, the relationships are not directly proportional and the equations become more complex. Absolute zero (0 K) is the point where the volume and pressure of an ideal gas would theoretically reach zero.

Q7. What is the ideal gas law? Answer: The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature.

Multiple Choice Questions (MCQs)

• Q1. Gas thermometers use the variation of:
• A. Color with temperature
• B. Electrical resistance with temperature
• C. Volume and pressure with temperature
• D. Mass with temperature

• Correct Answer: C
• Explanation: The text states that when a gas is heated, its volume as well as pressure may change, and these variations are used in gas thermometers.

• Q2. A constant-volume gas thermometer uses:
• A. Charles's Law
• B. Gay-Lussac's Law
• C. Ohm's Law
• D. Newton's Law

• Correct Answer: B
• Explanation: The text states that a constant-volume gas thermometer uses Gay-Lussac's law (P ∝ T at constant volume).

• Q3. A constant-pressure gas thermometer uses:
• A. Gay-Lussac's Law
• B. Charles's Law
• C. Ohm's Law
• D. Newton's Law

• Correct Answer: B
• Explanation: The text states that a constant-pressure gas thermometer uses Charles's law (V ∝ T at constant pressure).

• Q4. According to Gay-Lussac's Law, at constant volume:
• A. P ∝ 1T
• B. P ∝ T
• C. P ∝ T²
• D. P ∝ 1T²

• Correct Answer: B
• Explanation: Gay-Lussac's Law states that at constant volume, pressure is directly proportional to absolute temperature.

• Q5. According to Charles's Law, at constant pressure:
• A. V ∝ 1T
• B. V ∝ T
• C. V ∝ T²
• D. V ∝ 1T²

• Correct Answer: B
• Explanation: Charles's Law states that at constant pressure, volume is directly proportional to absolute temperature.

• Q6. In gas thermometers, temperature must be measured in:
• A. Celsius
• B. Fahrenheit
• C. Kelvin
• D. Rankine

• Correct Answer: C
• Explanation: The gas laws are based on absolute temperature, which is measured in Kelvin.

• Q7. The constant-volume gas thermometer is considered a primary standard because:
• A. It is cheap
• B. It relies on fundamental physical laws
• C. It is easy to use
• D. It measures color

• Correct Answer: B
• Explanation: The constant-volume gas thermometer relies on the gas laws, which are fundamental physical laws, making it a primary standard.

• Q8. Which gas law relates pressure and temperature at constant volume?
• A. Boyle's Law
• B. Charles's Law
• C. Gay-Lussac's Law
• D. Avogadro's Law

• Correct Answer: C
• Explanation: Gay-Lussac's Law relates pressure and temperature at constant volume.

• Q9. Which gas law relates volume and temperature at constant pressure?
• A. Boyle's Law
• B. Charles's Law
• C. Gay-Lussac's Law
• D. Avogadro's Law

• Correct Answer: B
• Explanation: Charles's Law relates volume and temperature at constant pressure.

• Q10. The ideal gas law is:
• A. PV = nRT
• B. P = IV
• C. F = ma
• D. E = mc²

Correct Answer: A Explanation: The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature.

Frequently Asked Questions (FAQs)

Q1. What is the difference between a gas thermometer and a liquid thermometer? Answer: A gas thermometer uses the change in volume or pressure of a gas with temperature. A liquid thermometer uses the change in volume of a liquid with temperature. Gas thermometers are generally more accurate and have a wider range, but they are more complex and bulky.

Q2. Why is the constant-volume gas thermometer more commonly used than the constant-pressure one? Answer: The constant-volume gas thermometer is simpler to operate and more accurate because it only requires the measurement of pressure (at a fixed volume). The constant-pressure thermometer requires a mechanism to maintain constant pressure while measuring volume, which is more complex.

Q3. What is the range of a gas thermometer? Answer: Gas thermometers can measure a very wide range of temperatures, from very low temperatures (close to absolute zero) to very high temperatures, depending on the gas used and the design of the thermometer. They are particularly useful for low-temperature measurements and for calibration.

Q4. Why do gas thermometers take a long time to respond? Answer: Gas thermometers take time to reach thermal equilibrium with the object being measured. The gas must absorb or release heat until its temperature matches the object's temperature. This process can be slow, especially for large gas bulbs.

Q5. What is the International Temperature Scale (ITS)? Answer: The International Temperature Scale (ITS) is an internationally agreed-upon temperature scale that defines the standard temperatures used for calibration. It is based on a set of fixed points (e.g., the freezing points of various metals) and the use of specified thermometers (including gas thermometers) for interpolation between these points. The ITS ensures that temperature measurements are consistent worldwide.

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