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 given values to SI units and define properties of air. Given: Initial volume, V_1 = 1 \, m^3 Initial temperature, T_1 = 15^ = 15 + 273.15 = 288.15 \, K Temperature after heating, T_2 = 300^ = 300 + 273.15 = 573.15 \, K Initial pressure, P_1 = 1.03 \, bar = 1.03 × 10^5 \, Pa For air (assumed ideal gas): Specific heat at constant pressure, c_p = 1.005 \, kJ/kg·K Specific heat at constant volume, c_v = 0.718 \, kJ/kg·K Gas constant, R = c_p - c_v = 1.005 - 0.718 = 0.287 \, kJ/kg·K = 287 \, J/kg·K Step 2: Calculate the mass of air (m). Using the ideal gas law at state 1: P_1 V_1 = m R T_1 m = (P_1 V_1)/(R T_1) = (1.03 × 10^5 \, Pa) × (1 \, m^3)(287 \, J/kg·K) × (2