This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Understand the relationship between volume and temperature. For a constant mass of gas maintained at constant pressure, the volume (V) is linearly related to the Celsius temperature (T_C). This relationship can be expressed as V = aT_C + b, where a and b are constants. Step 2: Use the given data points to find the constants a and b. We have two known points: 1. At T_C = 0^ C, V = 2.5 × 10^4. 2. At T_C = 100^ C, V = 3.15 × 10^4. Substitute the first point into the equation: 2.5 × 10^4 = a(0) + b b = 2.5 × 10^4 Substitute the second point and the value of b into the equation: 3.15 × 10^4 = a(100) + 2.5 × 10^4 100a = 3.15 × 10^4 - 2.5 × 10^4 100a = (3.15 - 2.5) × 10^4 100a = 0.65 × 10^4 a = (0.65 × 10^4)/(100) a = 0.65 × 10^2 a = 65 So, the relationship between volume and temperature is: V = 65T_C + 2.5 × 10^4 Step 3: Calculate the temperature corresponding to the boiling point of sulfur. We are given that the volume at the normal boiling point of sulfur is V = 6.52 × 10^4. Let this temperature be T_S. Substitute this volume into the derived equation: 6.52 × 10^4 = 65T_S + 2.5 × 10^4 65T_S = 6.52 × 10^4 - 2.5 × 10^4 65T_S = (6.52 - 2.5) × 10^4 65T_S = 4.02 × 10^4 T_S = (4.02 × 10^4)/(65) T_S = (40200)/(65) T_S ≈ 618.4615 Rounding to three significant figures, consistent with the input data: T_S ≈ 618^ C The temperature corresponding to the boiling point of sulfur is 618^ C.