Question

An ideal monatomic gas initially has a temperature of 330K and a pressure of 6.0 atm. It is to expand from volume 500 cm^3 to volume 1500 cm^3. If the expansion is isothermal, what are

a) the final pressure and
b) the work done by the gas?
If instead, the expansion is adiabatic, what are
c) the final pressure and
d) the work done by the gas?

Answer 1

To determine the final pressure and work done by the gas during an isothermal expansion, we can use the gas laws and the formula for work. For an adiabatic expansion, the final pressure is given by the formula P_final = P_initial * (V_initial / V_final)^(gamma), where gamma is the heat capacity ratio.

Step-by-step explanation:

To determine the final pressure and work done by the gas during an isothermal expansion, we can use the gas laws and the formula for work. For an isothermal process, the final pressure is equal to the initial pressure multiplied by the volume ratio. In this case, the final pressure is (initial pressure * initial volume) / final volume. The work done by the gas during an isothermal expansion is given by the equation W = (initial pressure * initial volume) * ln(final volume / initial volume).

For an adiabatic expansion, the final pressure is given by the formula P_final = P_initial * (V_initial / V_final)^(gamma), where gamma is the heat capacity ratio. The work done by the gas during an adiabatic expansion is given by the equation W = (P_initial * V_initial - P_final * V_final) / (gamma - 1).