A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if the Celsius temperature is doubled?

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Understand the relationship between temperature and volume for a gas at constant pressure. This is described by Charles's Law, which states that \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V \) is the volume and \( T \) is the absolute temperature in Kelvin.

Convert the initial temperature from Celsius to Kelvin. The formula for conversion is \( T(K) = T(°C) + 273.15 \). For \( T_1 = 100°C \), calculate \( T_1(K) = 100 + 273.15 \).

Double the Celsius temperature as stated in the problem. If the initial temperature is \( 100°C \), the new Celsius temperature is \( 2 \times 100 = 200°C \). Convert this to Kelvin: \( T_2(K) = 200 + 273.15 \).

Use Charles's Law to find the new volume \( V_2 \). Rearrange the equation to solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \). Substitute \( T_1 \) and \( T_2 \) in Kelvin into the equation.

Simplify the expression to determine the proportional change in volume. Since \( T_2 \) is double \( T_1 \), \( V_2 \) will also be double \( V_1 \). Thus, \( V_2 = 2 \times V_1 \).

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주요 개념

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Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when pressure is held constant. This means that if the temperature increases, the volume will also increase, and vice versa. The relationship can be expressed mathematically as V1/T1 = V2/T2, where V is volume and T is temperature.

Absolute Temperature

Absolute temperature is measured in Kelvin and is crucial for gas law calculations. It is obtained by adding 273.15 to the Celsius temperature. For example, 100°C corresponds to 373.15 K. Using absolute temperature ensures that the proportional relationships in gas laws are valid, as negative temperatures in Celsius do not make physical sense in this context.

Volume-Temperature Relationship

The volume-temperature relationship in gases indicates that if the temperature of a gas is doubled (in Kelvin), the volume will also double, provided the pressure remains constant. This principle allows us to predict how changes in temperature affect the volume of a gas, which is essential for solving problems involving gas behavior under varying thermal conditions.