Nitrogen gas in an expandable container is cooled from 50.0o C to 10.0o C with the pressure held constant at 3.00 X 105 Pa. The total heat liberated by the gas is 2.50 X 104 J. Assume that the gas may be treated as ideal. Find (a) the number of moles of gas; (b) the change in internal energy of the gas; (c) the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?
Solution 52P Problem (a) To find number of moles n Step 1: Initial Temperature of the gas T 1 = 50°C Final Temperature of the gas T 2 = 10°C Change in temperature dT = T - T2 1 = -40°C Constant pressure applied P = 3.00 x 10 Pa The total heat liberated by the gas Q = -2.50 x 10 J (Heat flows out of the gas) Step 2: For constant pressure Heat Liberated Q = nC dT P C P - Heat capacity at constant pressure, for Diatomic Nitrogen Gas C = R P 2 R - gas constant and value is 8.314 J/mol.K Step 3: Rearranging the above equation Q n = C .dT P Finally 2Q n = 7R.dT Step 4: 4 n = 2*(2.* 10 ) 7*8.3*4 (40) n = 21.48 mol number of moles n is 21.48 mol Problem (b) To find change in internal energy dU Step 1: dU = nRdT (no of degrees of freedom of nitrogen molecule is 5) 2 dU = 5 21.48 8.314 ( 40) 2 * * * 4 dU = -17.86 KJ or -1.79x 10 J 4 The change in internal energy dU is -1.79x 10 J Problem (c) To find the work done by the gas Step 1: W = Q - dU 4 4 W = -2.50 x 10 - (-1.79x 10 ) W = -2.50 x 10 + 1.79x 10 4 W = -7.1 x 10 J 3 The work done by the gas is -7.1 x 10 J Problem (d) Step 1: To find the heat liberated by the gas at constant volume Heat liberated Q = nC dT V 5 C V = R2