constant during the expansion. Recall from the 1st law of thermodynamics and energy conservation that (1) where is the change in the internal energy of the gas due to the change in heat, , it DU DQ receives and the work done on it, DW. Remember work here is defined as positive when the work is done on the gas and negative when the gas does work on (and therefore is lost to) the environment. Since DU is zero in an isothermal environment, (2) This means the heat added to the gas, goes directly into doing work done on the DQ, environment (the piston). Isentropic (Reversible adiabatic) expansion of the gas. For this step (C to D on Figure) the piston and cylinder are thermally insulated, so there is no heat transfer to or from the gas. The gas continues to expand, doing work on the surroundings. The gas expansion causes it to cool to the "cold" temperature, TC= T2 No heat is The internal energy of the gas is used to do work on the environment. (3) DW <0 so DU <0 Therefore the gas (Reversible) isothermal compression of the gas at the "cold" temperature, TC. (isothermal heat rejection) In this step (D to A on Figure), the environment (piston) does work on the gas by compressing it and reducing its volume. Again (2) applies (2) Since work is being done on the gas, > 0. Therefore <0. This means the gas is DW DQ losing quantity DQ2 of heat which is flowing from the gas into the low temperature reservoir. Isentropic compression of the gas. In this step (A to B in the Figure), the piston and cylinder are thermally insulated and this step is adiabatic. So as the environment does work on the gas and compresses it, (3) applies (3) > 0 so > 0 therefore the gas and its temperature rises to = DW DU TH T1. At this point the gas is in the same state as at the start of step 1.
constant during the expansion. Recall from the 1st law of thermodynamics and energy conservation that (1) where DU is the change in the internal energy of the gas due to the change in heat, DQ , it receives and the work done on it, DW. Remember work here is defined as positive when the work is done on the gas and negative when the gas does work on (and therefore is lost to) the environment. Since DU is zero in an isothermal environment, (2) This means the heat added to the gas, DQ, goes directly into doing work done on the environment (the piston). Isentropic (Reversible adiabatic) expansion of the gas. For this step (C to D on Figure) the piston and cylinder are thermally insulated, so there is no heat transfer to or from the gas. The gas continues to expand, doing work on the surroundings. The gas expansion causes it to cool to the "cold" temperature, TC= T2 No heat is The internal energy of the gas is used to do work on the environment. (3) DW <0 so DU <0 Therefore the gas (Reversible) isothermal compression of the gas at the "cold" temperature, TC. (isothermal heat rejection) In this step (D to A on Figure), the environment (piston) does work on the gas by compressing it and reducing its volume. Again (2) applies (2) Since work is being done on the gas, DW > 0. Therefore DQ <0. This means the gas is losing quantity DQ2 of heat which is flowing from the gas into the low temperature reservoir. Isentropic compression of the gas. In this step (A to B in the Figure), the piston and cylinder are thermally insulated and this step is adiabatic. So as the environment does work on the gas and compresses it, (3) applies (3) DW > 0 so DU > 0 therefore the gas and its temperature rises to TH = T1. At this point the gas is in the same state as at the start of step 1.
CarnotCycle.docx