Internal Energy, Heat, and Work Thermodynamics, Pressure & Volume, Chemistry Problems

This paragraph introduces the concept of internal energy changes in a system due to heat absorption and work done on or by the system. It explains the first law of thermodynamics in the context of chemistry, where the change in internal energy (ΔU) is equal to the heat added to the system (q) plus the work done on the system (w). The paragraph clarifies the signs of q and w in different processes: q is positive during endothermic processes (heat absorption) and negative during exothermic processes (heat release); w is positive when work is done on the system, increasing its internal energy, and negative when work is done by the system, decreasing its internal energy. The paragraph concludes with a worked example calculating the internal energy change when 300 joules of heat are absorbed and 400 joules of work are done on the system, resulting in a total increase of 700 joules in internal energy.

The second paragraph delves deeper into the application of the first law of thermodynamics with additional examples. It starts by illustrating the energy transfer between the system and surroundings using a diagram. The first scenario involves a system that releases 700 joules of heat and performs 300 joules of work, resulting in a decrease of 1000 joules in the system's internal energy. The paragraph then discusses a situation where the surroundings gain 250 joules of heat and 470 joules of work is performed by the surroundings, leading to an increase of 220 joules in the system's internal energy. The importance of visualizing energy transfer is emphasized, and the summary includes the correct interpretation of q and w in each case, adhering to the law of conservation of energy.

This paragraph focuses on calculating the work done by a gas when it expands or compresses against a constant external pressure. It begins by deriving the formula for work done on a gas, which is force times displacement, and then relates this to pressure, volume, and area. The explanation includes the concept that pressure is a type of potential energy stored in a gas, and that compressing a gas increases its pressure and internal energy, while expanding a gas decreases both. The paragraph uses a step-by-step approach to calculate the work done by a gas expanding from 25 liters to 40 liters against a constant external pressure of 2.5 atm, resulting in a negative work value of -37.5 liters*atm, which is then converted to joules for a complete understanding of energy transfer.

The fourth paragraph continues the discussion on work done by a gas, specifically during expansion and compression, and how it affects the internal energy of the system. It emphasizes that work done on the gas (compression) is positive, increasing the gas's internal energy, while work done by the gas (expansion) is negative, decreasing it. The relationship between the change in volume (ΔV) and work (w) is explored, with a negative sign convention explained for both processes. The paragraph provides a calculation example for the work required to compress a gas from 50 liters to 35 liters at a constant pressure of 8 atm, resulting in a positive work value of 12,156 joules, and reinforces the concept that energy is transferred during these processes.

The final paragraph presented in the script addresses a scenario where a gas absorbs heat energy from the surroundings and expands against a constant pressure, calculating the resulting change in internal energy. It uses the previously derived formula for work (w = -pΔV) to calculate the work done during the gas expansion from 30 liters to 70 liters against a pressure of 2.8 atm. The work done by the gas is found to be negative, indicating energy transfer to the surroundings. The paragraph then combines this work value with the heat absorbed (q = +500 joules) to determine the net change in internal energy (ΔU = q + w), which is a decrease of 10,845.6 joules, demonstrating the relationship between heat, work, and internal energy changes according to the first law of thermodynamics.