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 initial temperature from Celsius to Kelvin. To convert Celsius to Kelvin, add 273.15. T_1 = 127 \, ^ + 273.15 = 400.15 \, K Step 2: Identify the given values. Initial Volume (V_1) = 804 \, cm^3 Initial Temperature (T_1) = 400.15 \, K Final Volume (V_2) = 603 \, cm^3 Final Temperature (T_2) = ? Step 3: 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: (V_1)/(T_1) = (V_2)/(T_2) To find T_2, rearrange the formula: T_2 = (V_2 T_1)/(V_1) Step 4: Substitute the values and calculate T_2. T_2 = (603 \, cm^3) × (400.15 \, K)804 \, cm^3 T_2 = 241290.45 \, K · cm^3804 \, cm^3 T_2 ≈ 300.11 \, K Step 5: Convert the final temperature back to Celsius. T_2 \, (^) = T_2 \, (K) - 273.15 T_2 \, (^) = 300.11 \, K - 273.15 T_2 \, (^) ≈ 26.96 \, ^ The temperature at which the volume of the gas will be 603 \, cm^3 is approximately 27.0 \, ^. Last free one today — make it count tomorrow, or type /upgrade for unlimited.