A rigid container initially holds nitrogen gas at standard temperature and pressure. When 415 J of heat is supplied to the gas, its temperature increases by 10.0^ C . The volume of the container is (Given gas constant R=8.3 J K ⁻¹ mol ⁻¹ )

Step-by-step solution

Since the container is rigid, the volume is constant, making the process isochoric. For a diatomic gas like nitrogen ( N₂ ), the molar heat capacity at constant volume is C_v = 5 2 R . The heat supplied is given by Q = n C_v T . Substituting the given values: 415 = n ( 5 2 8.3 ) (10) 415 = n 20.75 10 415 = 207.5 n n = 2 mol At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 L . Therefore, the volume of the container is: V = n 22.4 = 2 22.4 = 44.8 L Answer: 44.8 L