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 temperatures from Celsius to Kelvin. To convert Celsius to Kelvin, add 273.15. T_1 = 27 \, ^ + 273.15 = 300.15 \, K T_2 = 20 \, ^ + 273.15 = 293.15 \, K Step 2: Identify the given values. Initial Volume (V_1) = 300 \, cm^3 Initial Pressure (P_1) = 600 \, kPa Initial Temperature (T_1) = 300.15 \, K Final Volume (V_2) = 200 \, cm^3 Final Temperature (T_2) = 293.15 \, K Final Pressure (P_2) = ? Step 3: Apply the Combined Gas Law. The Combined Gas Law states that for a fixed amount of gas, the ratio of the product of pressure and volume to the absolute temperature is constant: (P_1 V_1)/(T_1) = (P_2 V_2)/(T_2) To find P_2, rearrange the formula: P_2 = (P_1 V_1 T_2)/(T_1 V_2) Step 4: Substitute the values and calculate P_2. P_2 = (600 \, kPa) × (300 \, cm^3) × (293.15 \, K)(300.15 \, K) × (200 \, cm^3) P_2 = 52767000 \, kPa · cm^3 · K60030 \, K · cm^3 P_2 ≈ 878.99 \, kPa The pressure the gas would exert is approximately 879 kPa. 3 done, 2 left today. You're making progress.