Calculation of Isothermal Expansion Work and Internal Energy Change
What is the maximum work done during an isothermal and reversible expansion of a gas?
The maximum work done during the isothermal process is 5706 J based on the formula for calculating work in isothermal processes. However, considering the first law of thermodynamics and given that heat absorbed by the system is 10000 J, the work done should be equal to the heat absorbed (10000 J). Change in internal energy is zero in an isothermal process.
What is the internal energy change if 10000 joule of heat is absorbed?
The change in internal energy during an isothermal and reversible expansion of a gas is zero, as the temperature remains constant. The internal energy change is zero because the internal energy of an ideal gas is only a function of temperature and not volume. Therefore, in this scenario, the internal energy change remains zero.
To calculate the maximum work done in an isothermal and reversible expansion of a gas, you can use the formula W = nRT ln(Vf/Vi), where n is the number of moles, R is the gas constant, T is the temperature in kelvins, and Vf and Vi are the final and initial volumes respectively. In this case, the work done is approximately 5706 J based on the given data.
Regarding the internal energy change, since the process is isothermal, the change in internal energy, ΔEint, during the expansion is zero because the internal energy of an ideal gas is solely dependent on temperature and not volume. According to the first law of thermodynamics, the change in internal energy is equal to the heat absorbed minus the work done. Given that the heat absorbed is 10000 J and the change in internal energy is zero, the work done also equals the heat absorbed, which is 10000 J.
When a gas undergoes an isothermal and reversible expansion, the temperature remains constant throughout the process. This means that the work done is solely a result of the change in volume, as the pressure and temperature remain constant. The formula for calculating the work done in an isothermal process takes into account the initial and final volumes of the gas.
Internal energy, on the other hand, is a state function that depends only on the temperature of the system. In an isothermal expansion, where the temperature remains constant, the internal energy change is zero because there is no change in temperature. This principle is in line with the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
Therefore, in the given scenario where 10000 J of heat is absorbed by the system, and the process is isothermal and reversible, the work done during the expansion is equal to the heat absorbed. This exemplifies the conservation of energy principle in thermodynamics, where the heat added to the system is converted into work done by the system without any change in internal energy due to the constant temperature.