A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 20^ C ? ( R=8.31 ~J ~mol ⁻¹ ~K ⁻¹ )

Step-by-step solution

At STP, the volume of 1 mole of an ideal gas is 22.4 L . Given the volume of the cylinder is 44.8 L , the number of moles n of hydrogen gas is n = 44.8 22.4 = 2 moles . Hydrogen is a diatomic gas, so its molar heat capacity at constant volume C_V is given by C_V = f 2 R , where f = 5 is the degrees of freedom for a diatomic molecule. C_V = 5 2 8.31 J mol ⁻¹ K ⁻¹ = 20.775 J mol ⁻¹ K ⁻¹ . The heat required Q to raise the temperature by T = 20^ C (which is equivalent to 20 K ) at constant volume is Q = n C_V T . Q = 2