Given below are two statements regarding the use of a bomb calorimeter:
Statement-I: \(\Delta U\) can be measured by bomb calorimeter.
Statement-II: Heat is not transferred from calorimeter to surroundings.
Analysis of Each Statement:
Statement-I Analysis: A bomb calorimeter is designed to measure the change in internal energy (\(\Delta U\)) of a reaction that occurs at constant volume. Since no work is done by volume expansion, the heat change measured represents the change in internal energy.
Statement-II Analysis: In a bomb calorimeter, the system is designed to be adiabatic, meaning that ideally, no heat is transferred to or from the surroundings during the measurement. This isolation ensures that the heat measured is only due to the reaction itself.
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 ____