Using the first law of thermodynamics:
\[ \Delta U = Q + W \]
For an isothermal process, \(\Delta U = 0\), so \(Q = -W\).
\[ W = -P_{\text{ext}} \Delta V = -80 \times 10^3 \times (45 - 30) \times 10^{-3} = -1200 \, \text{J} \]
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