1. System A (Adiabatic System): In an adiabatic system, there is no heat exchange with the surroundings. During the combustion of methane, the heat generated cannot escape. This results in an increase in temperature within the system.
2. System B (Diathermic Container): In a diathermic container, heat can flow in and out of the system. During the combustion of methane, the heat generated escapes to maintain constant temperature.
Thus, in System A, the temperature rises, while in System B, the temperature remains the same.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
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: