From the ideal gas law:
\[ PV = nRT \]
Rearranging for volume:
\[ V = \left( \frac{nR}{P} \right) T \]
The slope of the line in the \( V-T \) graph for an isobaric process is proportional to \( \frac{1}{P} \). Therefore, we have:
\[ \text{Slope} \propto \frac{1}{P} \]
Comparing slopes:\[ (\text{Slope})_2 > (\text{Slope})_1 \quad \implies \quad P_2 < P_1 \]
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: