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: Convert the given temperatures from Celsius to Kelvin. The initial temperature T_1 = 50^. The final temperature T_2 = 80^. To convert Celsius to Kelvin, add 273.15 (or 273 for common approximations). We will use 273.15 for better accuracy. T_1 = 50^ + 273.15 = 323.15 K T_2 = 80^ + 273.15 = 353.15 K Step 2: Apply Charles's Law. Charles's Law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature. The formula is: (V_1)/(T_1) = (V_2)/(T_2) Where V_1 is the initial volume, T_1 is the initial absolute temperature, V_2 is the final volume, and T_2 is the final absolute temperature. We are given V_1 = 30 cm^3. We need to find the fractional increase in volume, which is (V_2 - V_1)/(V_1). Step 3: Calculate the ratio of volumes. From Charles's Law, we can write: (V_2)/(V_1) = (T_2)/(T_1) Substitute the Kelvin temperatures: (V_2)/(V_1) = 353.15 K323.15 K (V_2)/(V_1) ≈ 1.09279 Step 4: Calculate the fractional increase in volume. The fractional increase in volume is defined as change in volumeoriginal volume, which is (V_2 - V_1)/(V_1). This can be rewritten as (V_2)/(V_1) - (V_1)/(V_1) = (V_2)/(V_1) - 1. Using the ratio calculated in Step 3: Fractional increase = (V_2)/(V_1) - 1 Fractional increase = 1.09279 - 1 Fractional increase = 0.09279 Step 5: Round the result and compare with the options. Rounding 0.09279 to three decimal places gives 0.093. Comparing this to the given options: A) 0.009 B) 0.093 C) 0.910 D) 1.090 The calculated fractional increase matches option (B). The final answer is B