Write the equation for the work done during the compression of an ideal gas.
(N/A) The work done $W$ by or on a gas during a process is given by the integral $W = \int_{V_i}^{V_f} P \, dV$.
For an ideal gas undergoing an isothermal compression,the equation is $W = nRT \ln\left(\frac{V_f}{V_i}\right)$. Since it is compression,$V_f < V_i$,making $W$ negative (work done on the gas).
For an adiabatic compression,the equation is $W = \frac{nR(T_f - T_i)}{\gamma - 1} = \frac{P_f V_f - P_i V_i}{\gamma - 1}$,where $\gamma$ is the adiabatic index.
For an ideal gas undergoing an isothermal compression,the equation is $W = nRT \ln\left(\frac{V_f}{V_i}\right)$. Since it is compression,$V_f < V_i$,making $W$ negative (work done on the gas).
For an adiabatic compression,the equation is $W = \frac{nR(T_f - T_i)}{\gamma - 1} = \frac{P_f V_f - P_i V_i}{\gamma - 1}$,where $\gamma$ is the adiabatic index.
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