One of the methods for estimating the temperature at the center of the sun is based on the ideal gas law. If the center is assumed to be a mixture of gases whose average molar mass is \(2.0 \mathrm{~g} / \mathrm{mol}\), and if the density and pressure are \(1.4 \mathrm{~g} / \mathrm{cm}^{3}\) and \(1.3 \times 10^{9} \mathrm{~atm}\), respectively, calculate the temperature.

To determine the temperature at the center of the sun using Ideal Gas Law, we start with understanding and using the correct formula: The Ideal Gas Law: The equation used is To solve for temperature ( ), rearrange the Ideal Gas Law: Where 2.0 - Density: = 1400 8.314 J/(mol·K). Finally, calculate temperature: Completing the calculation provides the final temperature around (26 million)

Before calculations, it is vital to use the consistent units. To convert pressure from atmospheres (atm) to Pascals (Pa): 1 atm = 1.01325 × 10⁵ Pa. Multiply given pressure ( by this conversion factor: Pascal, ensures compatibility with the Ideal Gas Law. Accurate pressure conversion safeguards correct temperature calculations. This switch also underscores the need for unit precision across all scientific computations.

Density ( ) relates mass per unit volume. Here's the conversion: 1 g/cm³ = 1000 kg/m³. Given the density as g/cm³, multiply by to convert to kg/m³. For the sun's core, where density is critical, correctly converted density supports accurate assessment. It informs us about how tightly matter is packed, vital for temperature computation using Ideal Gas Law.

Molar mass ( ) denotes the mass of one mole of substance. Here the mixture has an average molar mass of 2.0 g/mol. For consistency, convert this to kilograms per mole (kg/mol): 2.0 g/mol is 0.002 kg/mol. Correct molar mass ensures the integrity of calculations within the Ideal Gas scenario. understanding molar mass links directly to the number of moles involved in the temperature equation.

The universal gas constant ( ) symbolized as incorporates the relation among pressure, volume, temperature, and moles. It is a consistent value across calculations and its exact value is 8.314 J/(mol·K). Including the R value in Ideal Gas computations reinforces the equation's utility, making it a universal constant connecting macroscopic and microscopic properties of gases. Note, maintaining unit integrity (J/(mol·K)) across elements in the computation guarantees attainment of correct results in physics and chemistry realms.