of 25^circ C and volume of 8 It. Accordingly , calculate the work done,heat Suppose that we have an ideal gas at a pressure of 10 atm , temperature gained (or released , change energy and change in enthalpy for each provided processes below: a. Isothermal expansion of the gas to 1 atm pressure. b. Adiabatic expansion of the gas to 1 atm pressure. c. The cooling of the gas at constant volume to 1 atm pressure.

To solve this problem, we need to use 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.<br /><br />Let's calculate the work done, heat gained (or released), change in energy, and change in enthalpy for each process:<br /><br />a. Isothermal expansion of the gas to 1 atm pressure:<br />- Since the process is isothermal, the temperature remains constant, and the internal energy change (ΔU) is zero.<br />- The work done by the gas during isothermal expansion can be calculated using the formula: W = nRTln(P1/P2), where n is the number of moles of gas, R is the ideal gas constant, T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure.<br />- The heat gained or released (Q) during an isothermal process is equal to the work done by the gas.<br /><br />b. Adiabatic expansion of the gas to 1 atm pressure:<br />- In an adiabatic process, there is no heat exchange between the system and its surroundings, so Q = 0.<br />- The work done by the gas during adiabatic expansion can be calculated using the formula: W = (P1V1^n - P2V2^n)/(n-1), where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the heat capacity ratio (Cp/Cv).<br />- The change in internal energy (ΔU) during an adiabatic process is equal to the work done by the gas.<br /><br />c. The cooling of the gas at constant volume to 1 atm pressure:<br />- Since the volume remains constant, the work done by the gas (W) is zero.<br />- The heat gained or released (Q) during this process can be calculated using the formula: Q = nCvΔT, where n is the number of moles of gas, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature.<br />- The change in internal energy (ΔU) during this process is equal to the heat gained or released by the gas.<br /><br />Please note that the specific values for the number of moles of gas (n) and the initial pressure and temperature are not provided in the question. If you have these values, you can substitute them into the formulas to calculate the work done, heat gained (or released), change in energy, and change in enthalpy for each process.