Binary polymer blends of polypropylene and polyamide 6 are immiscible. From a thermodynamic viewpoint this is due to \(\underline{\hspace{2cm}}\).
Step 1: Thermodynamic viewpoint on immiscibility.
When two substances are mixed, the free energy of mixing depends on both the enthalpy and entropy. If the enthalpy of mixing is very high or the entropy of mixing is very low, the free energy of mixing will be positive, leading to immiscibility.
Step 2: Analyzing the options.
- (A) low enthalpy of mixing: A low enthalpy of mixing would favor miscibility, not immiscibility. Hence, this is not the correct option.
- (B) high entropy of mixing: High entropy would also favor mixing, and would not explain immiscibility.
- (C) high enthalpy of mixing: A high enthalpy of mixing could make the free energy of mixing positive, but it does not explain the key thermodynamic factor in this case.
- (D) low entropy of mixing: A low entropy of mixing means that the system does not have enough disorder to drive the mixing, leading to immiscibility. This is the correct thermodynamic explanation for the immiscibility of polypropylene and polyamide 6.
Step 3: Conclusion.
The correct reason for the immiscibility of the polymer blends is low entropy of mixing, which results in a positive free energy of mixing and hence immiscibility.
Final Answer: (D) low entropy of mixing
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).