For a cyclic process, the change in internal energy (\(\Delta U\)) is zero. Therefore, the heat absorbed (\(\Delta Q\)) is equal to the work done (\(\Delta W\)), which is the area enclosed by the P-V curve. The area is calculated as:
\[ \Delta Q = \Delta W = \pi \times (140 \times 10^3) \, \text{Pa} \times (140 \times 10^{-6} \, \text{m}^3) \]
\[ \Delta Q = 61.6 \, \text{J} \]
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
Statement-1: \( \text{ClF}_3 \) has 3 possible structures.
Statement-2: \( \text{III} \) is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.
Which of the following options is correct?
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: