Handout7 - CBE2124, Levicky Chapter 8 and 9 Energy Balances...

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CBE2124, Levicky 1 Chapter 8 and 9 – Energy Balances Reference States . Recall that enthalpy and internal energy are always defined relative to a reference state (Chapter 7). When solving energy balance problems, it is therefore necessary to define a reference state for each chemical species in the energy balance (the reference state may be predefined if a tabulated set of data is used such as the steam tables). Example . Suppose water vapor at 300 o C and 5 bar is chosen as a reference state at which H ˆ is defined to be zero. Relative to this state, what is the specific enthalpy of liquid water at 75 o C and 1 bar? What is the specific internal energy of liquid water at 75 o C and 1 bar? (Use Table B. 7). Calculating changes in enthalpy and internal energy . H ˆ and U ˆ are state functions , meaning that their values only depend on the state of the system, and not on the path taken to arrive at that state. IMPORTANT : Given a state A (as characterized by a set of variables such as pressure, temperature, composition) and a state B , the change in enthalpy of the system as it passes from A to B can be calculated along any path that leads from A to B , whether or not the path is the one actually followed. Example . 18 g of liquid water freezes to 18 g of ice while the temperature is held constant at 0 o C and the pressure is held constant at 1 atm. The enthalpy change for the process is measured to be Δ H ˆ = - 6.01 kJ. What would the Δ H ˆ for the process be if, instead, the 18 g of water is first heated from 0 o C to 100 o C and entirely vaporized to steam at 100 o C and 1 atm, then liquified by compression from 1 atm to 10 atm at 100 o C, than cooled to - 200 o C
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CBE2124, Levicky 2 (during which step it freezes to ice) while being decompressed to a pressure of 1 atm, and finally thus formed 18 g of ice is heated from -200 o C and 1 atm to ice at 0 o C and 1 atm? Types of Paths . There are five types of paths for which we will learn to calculate enthalpy changes Δ H ˆ : 1). Changes in pressure ( p ) at constant temperature ( T ) and state of aggregation (i.e. no phase changes). 2). Changes in T at constant p and state of aggregation. 3). Phase changes (i.e. melting, condensation, evaporation, solidification, sublimation) at constant T and p . 4). Mixing steps (two liquids, gas in a liquid, solid in a liquid) at constant T and p . 5). Chemical reactions taking place at constant T and p . The overall path from a state A to a state B will be able to be expressed as a combination of the above five types of steps. Because enthalpy is a state function, the total change Δ H ˆ for passing from state A to state B can be calculated as the sum of the enthalpy changes Δ H ˆ j for the individual steps, Δ H ˆ = Δ H ˆ 1 + Δ H ˆ 2 + Δ H ˆ 3 + Δ H ˆ 4 j = 1, 2, … k (1) where k is the total number of steps used, for purposes of the calculation, to take the system from the initial state A to the final state B . Note that the steps used for the calculation do not need to correspond to the actual path taken by the system from A to B .
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Handout7 - CBE2124, Levicky Chapter 8 and 9 Energy Balances...

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