SUMMARY / RELATED TOPICS

An isothermal process is a change of a system, in which the temperature remains constant: ΔT =0. This occurs when a system is in contact with an outside thermal reservoir, the change in the system will occur enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is. In other words, in an isothermal process, the value ΔT = 0 and therefore the change in internal energy ΔU = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0. We can say that in isothermal processes T = constant Δ T = 0 d T = 0 while in adiabatic processes Q = 0. Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including structured machines, living cells; some parts of the cycles of some heat engines are carried out isothermally. In the thermodynamic analysis of chemical reactions, it is usual to first analyze what happens under isothermal conditions and consider the effect of temperature.

Phase changes, such as melting or evaporation, are isothermal processes when, as is the case, they occur at constant pressure. Isothermal processes are used and a starting point in analyzing more complex, non-isothermal processes. Isothermal processes are of special interest for ideal gases; this is a consequence of Joule's second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. Thus, in an isothermal process the internal energy of an ideal gas is constant; this is a result of the fact. Note that this is true only for ideal gases. In the isothermal compression of a gas there is work done on the system to decrease the volume and increase the pressure. Doing work on the gas increases the internal energy and will tend to increase the temperature. To maintain the constant temperature energy must leave the system as heat and enter the environment. If the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change.

For isothermal expansion, the energy supplied to the system does work on the surroundings. In either case, with the aid of a suitable linkage the change in gas volume can perform useful mechanical work. For details of the calculations, see calculation of work. For an adiabatic process, in which no heat flows into or out of the gas because its container is well insulated, Q = 0. If there is no work done, i.e. a free expansion, there is no change in internal energy. For an ideal gas, this means that the process is isothermal. Thus, specifying that a process is isothermal is not sufficient to specify a unique process. For the special case of a gas to which Boyle's law applies, the product pV is a constant if the gas is kept at isothermal conditions; the value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant. In other words, the ideal gas law pV = nRT applies. Therefore: p = n R T V = constant V holds; the family of curves generated by this equation is shown in the graph in Figure 1.

Each curve is called an isotherm. Such graphs are termed indicator diagrams and were first used by James Watt and others to monitor the efficiency of engines; the temperature corresponding to each curve in the figure increases from the lower left to the upper right. Log In thermodynamics, the reversible work involved when a gas changes from state A to state B is W A → B = − ∫ V A V B p d V For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, is indicated in purple in Figure 2 for an ideal gas. Again, p = nRT/V applies and with T being constant, the expression for work becomes: W A → B = − ∫ V A V B p d V = − ∫ V A V B n R T V d V = − n R T ∫ V A V B 1 V d V = − n R T ln ⁡ V B V A By convention, work is defined as the work on the system by its surroundings. If, for example, the system is compressed the work is positive and the internal energy of the system increases. Conversely, if the system expands, it does work on the surroundings and the internal energy of the system decreases.

It is worth

Al-Mu'addal ibn Ali ibn al-Layth was the Saffarid ruler of Zarang for a part of 911. In 890 al-Mu'addal and his brother al-Layth helped their father'Ali escape from imprisonment at the hands of the latter's uncle, the Saffarid amir Amr ibn al-Layth; the three of them fled to Khurasan. After'Ali died in 893, the brothers continued to serve Rafi'. In 896 they were captured by'Amr. Near the end of 908 al-Layth made a bid for power against'Amr's son and successor Tahir by occupying part of Zarang. Al-Mu'addal, taken hostage by Tahir, was released in early 909 after Tahir was unable to dislodge al-Layth in an attempt to induce the latter to give up his struggle. Al-Layth maintained his position and Tahir was forced to withdraw. Al-Layth was now amir. In the east, supporters of Tahir were causing unrest in Zabulistan, while in the west, the Turkish general Sebük-eri had transferred his allegiance from the Saffarids to the Abbasid caliph, resulting in the loss of Fars and Kerman. Al-Mu'addal was sent to restore order to Zabulistan.