For an isothermal reversible expansion, the work done \( W \) is given by:
\[ W = -2.303nRT \log \left(\frac{V_f}{V_i}\right) \]Given:
Substitute into the formula:
\[ W = -2.303 \times 5 \times 8.314 \times 300 \times \log \left(\frac{100}{10}\right) \] \[ W = -2.303 \times 5 \times 8.314 \times 300 \times \log(10) \]Since \( \log(10) = 1 \):
\[ W = -2.303 \times 5 \times 8.314 \times 300 \] \[ W = -28720.713 \, \text{J} \]Rounding to the nearest integer:
\[ W = -28721 \, \text{J} \]Thus, \( x = 28721 \).
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32