Figure E19.8 shows a pV-diagram for an ideal gas in which its absolute temperature at ?b is one-fourth of its absolute temperature at a . (a) What volume does this gas occupy at point ?b?? (b) How many joules of work was done by or on the gas in this process? Was it done by or on the gas? (c) Did the internal energy of the gas increase or decrease from ?a to ?b?? How do you know? (d) Did heat enter or leave the gas from ?a to ?b?? How do you know?
Solution 8E Problem (a) Step 1: 4 3 V a = 0.5L = 5x10 m T a = T T T b = 4 P = 1.5 atm or (1.5x 1.013x10 Pa) Step 2: Volume at Point b (V b) From Ideal gas equation PV a = nRT a PV b = nRT b Step 3: Dividing the above equations T b V b = T aV a V b = TT40.5 V = 0.125L or 1.25x10 m4 3 b 3 3 Volume at b is 0.125L or 0.125x10 m Problem (b) Step 1: Workdone W = P.dV = P.(V - V a) b W = 1.5x 1.013x10 *(0.125-0.5)*10 3 W = -56.98 J The negative sign indicates that the work is done on the system Problem (c) Step 1: Internal energy of the gas decreases as the temperature decreases from a to b. Internal energy of an ideal gas depends on temperature. Problem (d) Step 1: Heat leaves the gas from a to b. As already given temperature of gas at b is one-fourth of its temperature at a, heat is decreased which means heat leaves the gas.