Final answer:
An isothermal compression of an ideal gas at constant temperature results in an increase in pressure and the work done on the gas is given by W = -nRT ln(V2/V1). For adiabetic compression, there is no heat exchange and an increase in both pressure and temperature, following PVγ = constant. These processes require the ideal gas law and the specific heat capacities to calculate the thermodynamic changes.
Step-by-step explanation:
During an isothermal compression, a gas remains at constant temperature as its volume decreases. If we refer to the ideal gas law, PV = nRT, since temperature (T) and the number of moles (n) remain constant, and R is the universal gas constant, the pressure P of the gas must increase as the volume V decreases. The work done by the gas is negative because the gas is compressed, and it is calculated by integrating PdV over the change in volume. In an isothermal process for an ideal gas, this work can be expressed as W = -nRT ln(V2/V1).
For an ideal gas undergoing adiabatic compression, we have no heat exchange with the surroundings (Q=0), and the work done on the gas results in an increase in internal energy. The adiabatic condition follows the relation PVγ = constant, where γ (gamma) is the heat capacity ratio. This leads to a different expression for work done and involves changes in both pressure and temperature.
In both isothermal and adiabatic processes involving ideal gases, the equations of state and the specific heat capacities of the gas are used to determine the changes in all thermodynamic properties of the system.