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Consider an engine in which the working substance is 1.23 mol of an ideal gas fo

ID: 1419830 • Letter: C

Question

Consider an engine in which the working substance is 1.23 mol of an ideal gas for which = 1.41. The engine runs reversibly in the cycle shown on the PV diagram (see figure below). The cycle consists of an isobaric (constant pressure) expansion a at a pressure of 15.0 atm, during which the temperature of the gas increases from 300 K to 600 K, followed by an isothermal expansion b until its pressure becomes 3.00 atm. Next is an isobaric compression c at a pressure of 3.00 atm, during which the temperature decreases from 600 K to 300 K, followed by an isothermal compression d until its pressure returns to 15 atm. Find the work done by the gas, the heat absorbed by the gas, and the internal energy change of the gas, first for each part of the cycle and then for the complete cycle.

Work done by the gas:


Heat absorbed by the gas:


Internal energy change of the gas:

Ua

Ub

Uc

Ud

Utotal

Wa =   kJ Wb =   kJ Wc =   kJ Wd =   kJ Wtotal =   kJ

Explanation / Answer

Work done by the gas:

Wa = 1.23 * 8.314 * (600 - 300)

      = 3067.86 J   =   3.067 kJ

Wb =   1.23 * 8.314 * 600 * ln(5)

        =   9.875 kJ

Wc = - 1.23 * 8.314 * (600 - 300)

      = - 3067.86 J   =   - 3.067 kJ

Wd =   - 1.23 * 8.314 * 600 * ln(5)

        =   - 9.875 kJ

Wtotal   =   0 kJ

Heat absorbed by the gas:

Qa = 3/2 * 8.314 * 300 * 1.23 = 4.601 kJ

Qb =   9.875 kJ

Qc = - 4.601 kJ

Qd =   - 9.875 kJ

Qtotal = 0 kJ

Internal energy change of the gas:

Ua   = 4.601 - 3.067 = 1.534 kJ

Ub = 0 kJ

Uc =    - 1.534 kJ

Ud = 0 kJ

Utotal    =   0 kJ