Initially 0.900 mol of an ideal gas in a container occupies a volume of 3.40 l a
ID: 2202957 • Letter: I
Question
Initially 0.900 mol of an ideal gas in a container occupies a volume of 3.40 l at a pressure of 3.80 atm with an internal energy U1 = 410.4 J. The gas is cooled at a constant volume until its pressure is 2.60 atm. Then it is allowed to expand at constant pressure until its volume is 8.00 l. The final internal energy is U2 = 660.7 J. All processes are quasi static. Draw this process on a PV diagram. What is the work done by the gas? Calculate work done by an ideal gas. Find the heat added during this process.Explanation / Answer
The change of internal energy of an ideal gas is given by ?U = n · cv · ?T The heat capacity at constant volume of a monatomic ideal gas is cv = (3/2)·R So for this process: ?U = 1mol · (3/2) · 8.3145J/molK · (276K - 272K) = 49.887J ˜ 50J Change of internal energy equals heat transferred TO plus work done ON the gas: ?U = Q + W Hence: W = ?U - Q = 50J - 1010J = -960J So 960J of work are done BY the gas.