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
Hey Yano, this problem involves Charles's Law, not Boyle's Law, because it relates volume and temperature. Boyle's Law relates pressure and volume. The notation "v²" likely refers to the final volume, V_2. Step 1: State 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) Rearranging to solve for V_2: V_2 = V_1 × (T_2)/(T_1) Step 2: Convert temperatures from Celsius to Kelvin. Gas law calculations require temperatures to be in Kelvin. T_K = T_C + 273.15 Given: V_1 = 1 L T_1 = 27^ C T_2 = 40^ C Convert T_1: T_1 = 27^ C + 273.15 = 300.15 K Convert T_2: T_2 = 40^ C + 273.15 = 313.15 K Step 3: Substitute the values into the Charles's Law formula. V_2 = 1 L × 313.15 K300.15 K Step 4: Calculate the final volume, V_2. V_2 = 1 L × 1.043305... V_2 ≈ 1.04 L The final volume is: 1.04 L That's 2 down. 3 left today — send the next one.