Question
A monoatomic gas of 2.00 mole is initial at 300K. The gasundergoes the following cycle: 1) the gas is heated at constantvolume to a temperature of 800K, 2) it is then allowed to expandisothermally to its initial pressure, and 3) it is then compressedat constant pressure to its initial state. A. What is the heat in joule the gas absorbed respectivelyduring the three processes listed above? R=8.31J/mol*K B. What is the net work done by the gas? A monoatomic gas of 2.00 mole is initial at 300K. The gasundergoes the following cycle: 1) the gas is heated at constantvolume to a temperature of 800K, 2) it is then allowed to expandisothermally to its initial pressure, and 3) it is then compressedat constant pressure to its initial state. A. What is the heat in joule the gas absorbed respectivelyduring the three processes listed above? R=8.31J/mol*K B. What is the net work done by the gas?
Explanation / Answer
A.The number of moles of the monoatomic gas are n = 2.00 The gas is initially at a temperature T = 300 K 1)When the gas is heated at constant volume to a temperatureof 800K,then the heat absorbed by the gas is W1 = n * R * T Here,R = 8.314 J/mol/K or W1 = 2.00 * 8.314 * 800 = 13302.4 J 2)When the gas is allowed to expand isothermally to itsinitial pressure,then the heat absorbed by the gas is W2 = P * T Here,P = 1atm = 1.013 * 105 Pa and T = 300 K or W2 = 1.013 * 105 * 300 = 303.9 *105 J 3)When the gas is compressed at constant pressure to itsinitial state,then the heat absorbed by the gas is W3 = n * R * T = 2.00 * 8.314 * (800 - 300) =2.00 * 8.314 * 500 = 8314 J The heat in joule the gas absorbed respectively during thethree processes listed above is W = W1 + W2 + W3 = 13302.4 +303.9 * 105 + 8314 = 3.04 * 107 J B)The net work done by the gas is W = W2 - (W1 + W3) = 30390000- (13302.4 + 8314) = 3.03 * 107 J