A sample of air weighing 1.18 g occupies 1.0 10^3 cm ^3 when maintained at 300 K and 1.0 10^5 Pa . When 2.0 cal of heat is supplied to it at constant volume, its temperature rises by 1^ C . Determine the amount of heat required to raise the temperature of the air by 1^ C at constant pressure, given that the mechanical equivalent of heat is 4.2 10⁻⁷ erg cal ⁻¹ . Assume the air behaves as an ideal gas.

Step-by-step solution

Given P = 1.0 10^5 Pa , V = 1.0 10^3 cm ^3 = 1.0 10⁻³ m ^3 , and T = 300 K . Using the ideal gas equation PV = nRT , the value of nR is: nR = PV T = 1.0 10^5 1.0 10⁻³ 300 = 100 300 = 1 3 J K ⁻¹ The heat required at constant volume for T = 1^ C is Q_v = 2.0 cal . The heat required at constant pressure for the same temperature rise is Q_p = Q_v + W , where W is the work done by the gas. At constant pressure, W = nR T . For T = 1^ C = 1 K : W = 1 3 1 = 1 3 J Converting the work into calories using the mechanical equiv