Question

Integer type questions 13. A tall cylindrical vessel with gaseous nitrogen is located in a uniform gravitational field in which free fall acceleration due to gravity is equal to g(10 m/s?). The temperature of nitrogen varies along the height so that its density is throughout same. The temperature gradient was found to be n x 4.2 KI km. Value of n is h 4 is-for an adiabatic process of an ideal gas for which internal energy U ΞΚ

Answer 1

P = -rho g h delta p = -rho g delta h dp = -rho g d h rightarrow (1) p = n KT (gas eqn) dp = n k dT implies p = rho/ m R T dp = rho/ m R d T from eqn dp/dh = -rho g from eq (1) and eqn (2). - rho R/ m dT = rho g d h dT/ dh = -g M/ R implies -84 k/km 34 = 4.2 times n n = 8.09 1 = 8 n = 8