\( q = 0, \, \Delta T = 0, \, w = 0 \)
\( q = 0, \, \Delta T<0, \, w \neq 0 \)
During free expansion of an ideal gas under adiabatic conditions, there is no transfer of heat, no work is done, and the temperature remains constant.
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