compression at 297K. During the sion,2090 J of heat energy are transferred to the gas Determine(a) the work performed by the gas during the isothermal expansion, (b) the heat rejected from the gas during the isothermal compression, and(c) the work done on the gas during th isothermal compression (a)According to the first law of thermodynamics, the work performed by the gas during the isothermal expansion is W=0=2090J (b) The efficiency of the Carnot heat engine is a so the heat rejected from the gas during the isothermal compression g|==00207-1506(0 According to the first law of thermodynamics, the work done on the gas during the isothermal compression is w= =150663J 2. One(1.00) mole of an ideal diatomic gas(with r 1.40)initially at 20.0C and 1.00 atm pressure is taken Pressure(atm) around the following cycle(see Figure 3) R Isothermal process Path(1): an isochoric increase in pressure until the temperature of the gas is 150.C and the pressure is 1.00 2 P Path(): an isothermal expansion until the pressure Volume returns to 1. 00 atm Path ( 3): an isobaric compression until the gas Fig 3 ginal volume. (a)What is the original volume of the gas at the beginning and end of the cycle? (b) What is the pressure of the gas at the completion of path(1)? the volume of the gas at the completion of path(2)? And the temperature of the gas at the completion of path (2)? (c)Calculate the work done by the gas during each path of the cycle and the total work done by the gas. And the heat transfer to the gas during each path of the cycle and the total heat transfer to the gas over the cycle (d) Find the efficiency of the cycle (e) Calculate the maximum efficiency that a heat engine could have if it operated between the hottest and coldest temperature encountered by this gas in this cyclecompression at 297K. During the expansion, 2090 J of heat energy are transferred to the gas. Determine (a) the work performed by the gas during the isothermal expansion, (b) the heat rejected from the gas during the isothermal compression, and (c) the work done on the gas during the isothermal compression. Solution: (a) According to the first law of thermodynamics, the work performed by the gas during the isothermal expansion is W = Q = 2090 J. (b) The efficiency of the Carnot heat engine is H C H C H T T Q Q Q W ε = =1− =1− so the heat rejected from the gas during the isothermal compression is 1506.63 (J) 412 297 = ⋅ = 2090× = H C C H T T Q Q According to the first law of thermodynamics, the work done on the gas during the isothermal compression is = =1506.63 J W QC 2. One (1.00) mole of an ideal diatomic gas (with γ = 1.40) initially at 20.0 °C and 1.00 atm pressure is taken around the following cycle (see Figure 3). Path (1): an isochoric increase in pressure until the temperature of the gas is 150 °C and the pressure is P; Path (2): an isothermal expansion until the pressure returns to 1.00 atm. Path (3): an isobaric compression until the gas reaches its original volume. (a) What is the original volume of the gas at the beginning and end of the cycle? (b) What is the pressure of the gas at the completion of path (1)? the volume of the gas at the completion of path (2)? And the temperature of the gas at the completion of path (2)? (c)Calculate the work done by the gas during each path of the cycle and the total work done by the gas. And the heat transfer to the gas during each path of the cycle and the total heat transfer to the gas over the cycle. (d) Find the efficiency of the cycle. (e) Calculate the maximum efficiency that a heat engine could have if it operated between the hottest and coldest temperature encountered by this gas in this cycle. Solution: A V P 1 2 3 Fig.3 1.00 Pressure (atm) Volume Isothermal process B C