A quantity of an ideal gas is compressed to half" its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.
doesn't adiabatic mean no work, so it would be the least, correct? and what about the other two?
No, "adiabatic" means no heat is added or removed. The heating that results from compression will make this case require the most work.
An isothermal compression will require that the pressure decreases during the compression, since p = RT/V and T stays the same
Work done on the gas is the integral of -p dV . You will get the smallest integral when p decreases.
Yes, you are correct that an adiabatic process implies no transfer of heat. In an adiabatic compression, the work is done solely by the external agent to decrease the volume of the gas without any heat exchange. Therefore, the adiabatic process would require the least amount of work from an external agent.
Now, let's consider the other two processes: isothermal and isobaric.
In an isothermal process, the temperature of the gas remains constant throughout the compression, meaning the gas is heated or cooled in order to maintain a constant temperature. In this case, work is required to compress the gas and counterbalance the heat transfers occurring to keep the temperature constant. Since work is involved in both compression and heat transfer, the work required in an isothermal process is higher than in an adiabatic process.
On the other hand, in an isobaric process, the pressure of the gas remains constant while its volume is being compressed. In this case, work is only done to decrease the volume of the gas, without any heat transfer. Although the work required to compress the gas is higher than in an adiabatic process, it is generally lower than in an isothermal process, where energy is also utilized to counterbalance heat transfer.
Therefore, the order of the work required, from least to greatest, is: adiabatic, isobaric, isothermal.