A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in Figure 5.4. When 0.49 kJ of heat is added to the gas, it expands and does 214 J of work on the surroundings. What are the values of H and E for this process?

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Identify the given values: the heat added to the system \( q = 0.49 \text{ kJ} \) and the work done by the system \( w = 214 \text{ J} \).

Convert all units to the same system for consistency. Since \( q \) is given in kJ, convert \( w \) from J to kJ: \( 1 \text{ kJ} = 1000 \text{ J} \).

Use the first law of thermodynamics, which states \( \Delta E = q - w \), to find the change in internal energy \( \Delta E \).

Calculate the change in enthalpy \( \Delta H \) using the relationship \( \Delta H = \Delta E + P\Delta V \). Since the process occurs at constant pressure, \( \Delta H = q \).

Substitute the known values into the equations to find \( \Delta E \) and \( \Delta H \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a gas expanding in a cylinder, the internal energy change (ΔE) of the system is equal to the heat added to the system (q) minus the work done by the system (w) on the surroundings, expressed as ΔE = q - w.

Enthalpy (H)

Enthalpy is a thermodynamic quantity that represents the total heat content of a system at constant pressure. It is defined as H = E + PV, where E is the internal energy, P is the pressure, and V is the volume. In processes occurring at constant pressure, the change in enthalpy (ΔH) can be directly related to the heat exchanged with the surroundings.

Work Done by a Gas

In thermodynamics, the work done by a gas during expansion is calculated as the product of pressure and the change in volume (w = PΔV). When a gas expands against a constant external pressure, it does work on the surroundings, which must be accounted for when calculating changes in internal energy and enthalpy.

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