Cyclic processes and their effeciency, Carnot cycle Homework

Homework (Revision Problems)

1.      A heat engine consists of a coal‑fired steam turbine driving an electric power generator with a power output of 120 megawatts. The thermal efficiency of the heat engine is 40 percent.

a.       Determine the time rate at which heat is supplied to the engine.

b.      If the heat of combustion of coal is 4.4 x 10⁷ joules per kilogram, determine the rate in kilograms per second at which coal is burned.

c.       Determine the time rate at which heat is discarded by the engine.

2.      A heat engine operating between temperatures of 500 K and 300 K is used to lift a 10‑kilogram mass vertically at a constant speed of 4 meters per second.

a.   Determine the power that the engine must supply to lift the mass.

b.   Determine the maximum possible efficiency at which the engine can operate.

c.   If the engine were to operate at the maximum possible efficiency, determine the following.

      i. The rate at which the hot reservoir supplies heat to the engine

      ii. The rate at which heat is exhausted to the cold reservoir

3.      One mole of an ideal monatomic gas is taken through the cycle abca shown on the diagram below. 

1.      State a has volume V_a = 17 × 10^–3 cubic meter and pressure P_a = 1.2 × 10⁵ pascals, and state c has volume V_c = 51 × 10^–3 cubic meter.  Process ca lies along the 250 K isotherm.  Determine each of the following.

a.         The temperature T_b of state b

b.         The heat Q_ab added to the gas during process ab

c.         The change in internal energy U_b ‑ U_a

d.         The work W_bc done by the gas on its surroundings during process bc

The net heat added to the gas for the entire cycle 1,800 joules.  Determine each of the following.

e.     The net work done on the gas by its surroundings for the entire cycle

f.    The efficiency of a Carnot engine that operates between the maximum and minimum temperatures in this cycle