All of the following options consist of various laws and statements. Among all the options, only one law and its statement is correctly written. Identify the correct option.
Charles’ law states that if any gas is heated at constant pressure, its volume changes directly as its absolute temperature.
Identifying the Correct Gas Law Statement
The question asks us to identify the single option among the given choices that correctly states a physical law related to gases.
Let's analyze each option provided:
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Option 1: Joule’s law states that the volume of a given mass of a perfect gas varies inversely as the absolute pressure when temperature is constant.
This statement describes Boyle's Law, not Joule's Law. Boyle's Law states that for a fixed mass of an ideal gas at constant temperature, the pressure and volume are inversely proportional ($\text{PV} = \text{constant}$). Joule's Law is primarily associated with the heat produced by electric current flowing through a resistor ($H = I^2Rt$) or, in thermodynamics, the internal energy of an ideal gas being dependent only on temperature (Joule's Second Law of Thermodynamics).
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Option 2: Boyle’s law states that the specific internal energy of a gas depends only on the temperature of the gas and is independent of both, pressure and volume.
This statement describes a characteristic of an ideal gas, often associated with Joule's Second Law of Thermodynamics, not Boyle's Law. As mentioned above, Boyle's Law relates pressure and volume at constant temperature.
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Option 3: Charles’ law states that if any gas is heated at constant pressure, its volume changes directly as its absolute temperature.
This is a correct statement of Charles's Law. Charles's Law states that for a fixed mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature ($\frac{V}{T} = \text{constant}$).
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Option 4: Amagat’s law states that the pressure of a mixture of gases is equal to the sum of the partial pressures of the constituents.
This statement describes Dalton's Law of Partial Pressures, not Amagat's Law. Dalton's Law states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component gas in the mixture. Amagat's Law (also known as the Law of Partial Volumes) states that the total volume of a mixture of gases is equal to the sum of the partial volumes of the component gases, assuming the temperature and pressure remain constant.
Based on the analysis, only the statement regarding Charles's Law in Option 3 is correctly written.
Here is a summary comparing the laws mentioned:
| Law | Correct Statement | Condition | Mathematical Relation (Ideal Gas) |
|---|---|---|---|
| Boyle's Law | Volume is inversely proportional to pressure. | Constant temperature and mass. | $\text{PV} = \text{constant}$ |
| Charles's Law | Volume is directly proportional to absolute temperature. | Constant pressure and mass. | $\frac{\text{V}}{\text{T}} = \text{constant}$ |
| Joule's Second Law (Thermodynamics) | Internal energy of an ideal gas depends only on temperature. | Ideal Gas | $\text{U} = f(\text{T})$ |
| Dalton's Law | Total pressure is sum of partial pressures. | Mixture of non-reacting gases | $\text{P}_{\text{total}} = \sum \text{P}_{\text{i}}$ |
| Amagat's Law | Total volume is sum of partial volumes. | Mixture of non-reacting gases at same T, P | $\text{V}_{\text{total}} = \sum \text{V}_{\text{i}}$ |
Reviewing the options against the correct definitions, Option 3 accurately states Charles's law.
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