This scenario describes a process known as free expansion. In free expansion, the gas expands into a vacuum (another vessel that is evacuated), and the system is insulated, meaning no heat is exchanged with the surroundings (adiabatic process).
In an adiabatic process with an ideal gas, there is no heat exchange (\( Q = 0 \)) and no work done by or on the gas if there is no external pressure opposing the expansion.
Therefore, the correct answer is:
\[ \boxed{\text{C) The volume of the gas is doubled}} \]
\[ f(x) = \begin{cases} x\left( \frac{\pi}{2} + x \right), & \text{if } x \geq 0 \\ x\left( \frac{\pi}{2} - x \right), & \text{if } x < 0 \end{cases} \]
Then \( f'(-4) \) is equal to:If \( f'(x) = 4x\cos^2(x) \sin\left(\frac{x}{4}\right) \), then \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:
Let \( f(x) = \frac{x^2 + 40}{7x} \), \( x \neq 0 \), \( x \in [4,5] \). The value of \( c \) in \( [4,5] \) at which \( f'(c) = -\frac{1}{7} \) is equal to:
The general solution of the differential equation \( \frac{dy}{dx} = xy - 2x - 2y + 4 \) is:
\[ \int \frac{4x \cos \left( \sqrt{4x^2 + 7} \right)}{\sqrt{4x^2 + 7}} \, dx \]