Match List-I with List-II.
The relations for heat exchange and work done during thermodynamic processes are:
- (A) Isobaric: In an isobaric process (constant pressure), the heat supplied to the system is equal to the work done by the system, i.e., \( \Delta Q = \Delta W \).
- (B) Isochoric: In an isochoric process (constant volume), the change in heat is equal to the change in internal energy, i.e., \( \Delta Q = \Delta U \).
- (C) Adiabatic: In an adiabatic process (no heat exchange), \( \Delta Q = 0 \).
- (D) Isothermal: In an isothermal process (constant temperature), the change in heat is equal to the change in internal energy plus the work done by the system, i.e., \( \Delta Q = \Delta U + P \Delta V \).
Thus, the correct answer is (3).
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 ____
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: