What is the change in enthalpy for an isothermal, isentropic compression of an ideal gas from 2 atm to 12 atm?
To find the change in enthalpy for an isothermal, isentropic compression of an ideal gas, we need to use the ideal gas law and specific heat capacity relationships.
Step 1: Determine the initial and final states of the gas.
In this case, the gas is compressed from an initial pressure of 2 atm to a final pressure of 12 atm. The compression process is isothermal, meaning the temperature remains constant.
Step 2: Use the ideal gas law to find the initial and final volumes.
The ideal gas law relates the pressure (P), volume (V), and temperature (T) of a gas: PV = nRT, where n is the number of moles of gas, and R is the gas constant.
Since the process is isothermal, the temperature remains constant. Therefore, we can write:
P1V1 = P2V2
Step 3: Find the change in volume.
Rearrange the equation from Step 2 to solve for the change in volume:
ΔV = V2 - V1 = (P1V1 - P2V2) / P2
Step 4: Calculate the change in enthalpy.
The change in enthalpy (ΔH) can be calculated using the equation:
ΔH = nCpΔT
where n is the number of moles of gas, Cp is the specific heat capacity at constant pressure, and ΔT is the change in temperature.
Since the process is isentropic, the change in temperature (ΔT) is zero. Therefore, the change in enthalpy for an isentropic process is zero.
In this case, an isothermal process is also adiabatic and reversible, which means there are no heat transfer and no energy losses due to friction, so the change in enthalpy is also zero.
Therefore, the change in enthalpy for an isothermal, isentropic compression of an ideal gas from 2 atm to 12 atm is zero.