Question

Two moles of oxygen gas are contained in a piston and cylinder device. Initially the gas is at 300. K and sufficient weight is placed on the piston so that the pressure is 2.0 bar. Consider two different processes in which 2000. J of energy in the form of heat are added to the gas in the device. In the second process, the piston is allowed to move freely so that the pressure remains constant. What are the final temperature and volume of the gas? Tf =334.36 K; V =0.0278 m3 . For both cases, assume that the oxygen behaves as an ideal gas

Answer 1

Given data Number of moles of gas n-2 Initial temperature T 300 K Initial pressure R 2.0 bar Heat added to the gas dQ 1000 J Process 1: When volume remain constant The molar heat capacity at constant pressure for oxygen Cp 29.38 J/mol-K Write the expression to determine the molar heat capacity at constant volume Here, R -8.314J/mol-K is the gas constant Substitute the values in the above equation. 29.38-C 8.314 C, = 21.066 J/mol-K At constant volume, the work done on the system is zero therefore, dV = do - 2000 J Write the expression to determine the final temperature of the gas dUU Substitute the values in the above equation. 2000 2x21.066 - 47.47 +300 = 347.47 K +300 As the gas behaves like an ideal gas therefore,

R P Substitute the values in the above equation 347.47 300 2.32 bar Hence, in the first process, the final temperature and pressure of the gas are |347.47 KI and 2.32 bar respectively Process II: When Pressure remains constant Write the expression to calculate the final temperature of the gas 2 Substitute the values in the above equation 2x29.38 34.036+300 334.036K As the gas behaves like an ideal gas therefore, nRT Substitute the values in the above equation

2x0.0831x334.036 2.0 -27.76 L 27.76 3 1000 0.0278 m Hence, in the second process, the final temperature and volume of the gas are 334.036 K] and 0.0278 mrespectively