1.Pleased begin with the definition for Molar Pdv Work [Eq. Trigger] and the Ideal Gas Law [Eq. Bullet]: \bar{w}=-\int_{\bar{v}_{1}}^{\bar{v}_{2}} P d \bar{v}(E q, T r i g g e r) \quad \text { and } \quad P \bar{v}=\bar{R} T(E q, B u l l e t) Please solve Eq. Bullet for pressure and use the resulting express to eliminate pressure from Eq. Trigger.Let T constant and show that \bar{w}=-\bar{R} T \int_{\bar{v}_{1}}^{\bar{v}_{2}} \frac{d \bar{v}}{\bar{v}} E q \cdot \text { Pistol } Please integrate Eq. Pistol and evaluate between the limits to show that \bar{w}=-\bar{R} T \ln \left(\frac{\bar{\nu}_{2}}{\bar{v}_{1}}\right)

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6