$$X_{\text { work }}=\left\{\begin{array}{ll}{W-W_{\text { surr }}} & {\text { (for boundary work) }} \\ {W} & {\text { (for other forms of work) }}\end{array}\right.$$
where $$W_{\text { surr }}=P_{0}\left(V_{2}-V_{1}\right), P_{0}$$ is atmospheric pressure, and $$V_{1}$$ and $$V_{2}$$ are theinitial and final volumes of the system.
Exergy transfer by mass:
$$\quad X_{\text { mass }}=m \psi$$
where $$\psi=\left(h-h_{0}\right)-T_{0}\left(s-s_{0}\right)+V^{2} / 2+g z$$
$$\quad X_{\text { heat }}=\left(1-\frac{T_{0}}{T}\right) Q \quad(\mathrm{kJ})$$
When the temperature T is constant
$$X_{\mathrm{heat}}=\int\left(1-\frac{T_{0}}{T}\right) \delta Q$$
When the temperature T is not constant
$$X_{\text { work }}=\left\{\begin{array}{ll}{W-W_{\text { surr }}} & {\text { (for boundary work) }} \\ {W} & {\text { (for other forms of work) }}\end{array}\right.$$
where $$W_{\text { surr }}=P_{0}\left(V_{2}-V_{1}\right), P_{0}$$ is atmospheric pressure, and $$V_{1}$$ and $$V_{2}$$ are theinitial and final volumes of the system.
$$\quad X_{\text { mass }}=m \psi$$
where $$\psi=\left(h-h_{0}\right)-T_{0}\left(s-s_{0}\right)+V^{2} / 2+g z$$
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