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

Verified step by step guidance

1. Identify the initial conditions and the final condition. Initially, the temperature is 100°C, which needs to be converted to Kelvin. The Kelvin temperature is given by T₁ = 100°C + 273.15 = 373.15 K.
2. Understand that the problem states the pressure is held constant and the Kelvin temperature is doubled. Therefore, the final temperature T₂ = 2 × T₁ = 2 × 373.15 K.
3. Recall the ideal gas law in the form of Charles's Law, which states that for a given mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature (V ∝ T).
4. Set up the proportion based on Charles's Law: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ where V₁ is the initial volume V₀, T₁ is the initial temperature, V₂ is the final volume, and T₂ is the final temperature.
5. Solve the proportion for V₂: V₂ = V₀ × $\frac{T_2}{T_1}$. Substitute the values of T₁ and T₂ to find the expression for V₂ in terms of V₀.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental in understanding how gases behave under varying conditions. In this scenario, with constant pressure, changes in temperature directly affect the volume of the gas.

Temperature Scales

Temperature can be measured in different scales, with Celsius and Kelvin being the most common in physics. The Kelvin scale is an absolute temperature scale where 0 K represents absolute zero, the point at which molecular motion ceases. To convert Celsius to Kelvin, one adds 273.15, making it crucial to use Kelvin when applying gas laws.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant. This means that if the temperature increases, the volume must also increase, provided the pressure does not change. In this question, doubling the Kelvin temperature will lead to a corresponding increase in volume.