For a cyclic process, the change in internal energy (\(\Delta U\)) is zero. Therefore, the heat absorbed (\(\Delta Q\)) is equal to the work done (\(\Delta W\)), which is the area enclosed by the P-V curve. The area is calculated as:
\[ \Delta Q = \Delta W = \pi \times (140 \times 10^3) \, \text{Pa} \times (140 \times 10^{-6} \, \text{m}^3) \]
\[ \Delta Q = 61.6 \, \text{J} \]
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: