Step 1: Understand the behavior of polymer crystals.
Polymer crystals are not as regular as small molecular crystals, which results in a range of melting points. This is because the polymer chains, being large and flexible, can adopt different configurations that are not in equilibrium, thus leading to multiple melting points.
Step 2: Analyze the options.
- (A) absence of intermolecular interactions: Polymers do have intermolecular interactions, so this is incorrect.
- (B) absence of long-range ordering: This is not the main reason for the range of melting points. Polymers do exhibit some long-range ordering in the crystalline phase.
- (C) polymer chains are not in thermodynamic equilibrium in a metastable state: This is correct because the polymer chains can be in a metastable state, leading to a distribution of melting points.
- (D) melting behavior of polymer crystal is independent of sample thermal history: This is incorrect, as the thermal history does affect the melting behavior.
Step 3: Conclusion.
The reason for the range of melting points in polymer crystals is due to the polymer chains not being in thermodynamic equilibrium, leading to metastable states.
Final Answer: \text{(C) the polymer chains are not in thermodynamic equilibrium in a metastable state}
Potato slices weighing 50 kg is dried from 60% moisture content (wet basis) to 5% moisture content (dry basis). The amount of dried potato slices obtained (in kg) is ............ (Answer in integer)
Two Carnot heat engines (E1 and E2) are operating in series as shown in the figure. Engine E1 receives heat from a reservoir at \(T_H = 1600 \, {K}\) and does work \(W_1\). Engine E2 receives heat from an intermediate reservoir at \(T\), does work \(W_2\), and rejects heat to a reservoir at \(T_L = 400 \, {K}\). Both the engines have identical thermal efficiencies. The temperature \(T\) (in K) of the intermediate reservoir is ........ (answer in integer). 
A bar of length \( L = 1 \, {m} \) is fixed at one end. Before heating its free end has a gap of \( \delta = 0.1 \, {mm} \) from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of \( 10^\circ {C} \). The coefficient of linear thermal expansion of the material is \( 20 \times 10^{-6} / \degree C \) and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature.
The magnitude of the resulting axial stress on the bar is .......... MPa (in integer). 
A massless cantilever beam, with a tip mass \( m \) of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length \( L = 1 \, {m} \), with a circular cross-section of diameter \( d = 20 \, {mm} \). The Young’s modulus of the beam material is 200 GPa.
The natural frequency of the spring-mass system is ............ Hz (rounded off to two decimal places).
A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm\(^2\), area moment of inertia of 7854 mm\(^4\), and a length \( L \) of 4 m. A point load \( P = 100 \, {N} \) acts at the center and an axial load \( Q = 20 \, {kN} \) acts through the centroidal axis as shown in the figure.
The magnitude of the offset between the neutral axis and the centroidal axis, at \( L/2 \) from the left, is ............ mm (rounded off to one decimal place).