The air within a piston equipped with a cylinder absorbs 565 J of heat and expands from an initial volume of 0.10 L to a final volume of 0.85 L against an external pressure of 1.0 atm. What is the change in internal energy of the air within the piston?

Verified step by step guidance

1. Identify the given values: heat absorbed (q) = 565 J, initial volume (V_i) = 0.10 L, final volume (V_f) = 0.85 L, and external pressure (P) = 1.0 atm.
2. Recall the first law of thermodynamics: \( \Delta U = q - w \), where \( \Delta U \) is the change in internal energy, \( q \) is the heat absorbed, and \( w \) is the work done by the system.
3. Calculate the work done by the system using the formula \( w = P \Delta V \), where \( \Delta V = V_f - V_i \). Convert the pressure from atm to J by using the conversion factor: 1 L·atm = 101.3 J.
4. Substitute the values into the work formula: \( w = 1.0 \text{ atm} \times (0.85 \text{ L} - 0.10 \text{ L}) \times 101.3 \text{ J/L·atm} \).
5. Substitute the values of \( q \) and \( w \) into the first law of thermodynamics equation to find \( \Delta U \): \( \Delta U = 565 \text{ J} - w \).

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In a closed system, the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W). This principle is essential for analyzing energy changes in thermodynamic processes.

Work Done by a Gas

In thermodynamics, work done by a gas during expansion is calculated as W = PΔV, where P is the external pressure and ΔV is the change in volume. When a gas expands against an external pressure, it does work on the surroundings, which must be accounted for when determining the change in internal energy.

Units of Energy

Energy in thermodynamics is often measured in joules (J) or liters-atmospheres (L·atm). When calculating work done by a gas, it is important to ensure that units are consistent. For example, converting L·atm to joules (1 L·atm = 101.3 J) may be necessary to accurately compute the change in internal energy.