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Distillation under very reduced pressure is called:
Vacuum distillation lowers boiling points, used for heat-sensitive compounds.
Two cars P and Q start simultaneously from the same point. Their positions are $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do they have equal velocities?
$v_P = a + 2bt$, $\quad v_Q = f - 2t$
Setting equal: $a + 2bt = f - 2t \Rightarrow 2t(b+1) = f-a \Rightarrow t = \mathbf{\dfrac{f-a}{2(1+b)}}$
Modern democracy rests on a tension that has never been satisfactorily resolved: it commits itself simultaneously to the principle that all citizens are equal participants in political decision-making and to the undeniable reality that governance of complex societies requires specialized knowledge that most citizens do not possess. This tension is particularly acute in an era of climate science, epidemiology, and monetary policy — domains in which the gap between expert consensus and popular understanding may be decisive for human welfare.
The classical response to this tension, associated with John Dewey among others, holds that the solution lies not in deferring to experts but in educating the public to the point where democratic deliberation becomes genuinely informed. A self-governing society, on this view, must invest heavily in the democratic capacity of its citizens. The difficulty is that the explosion of specialized knowledge in the twentieth and twenty-first centuries has made this aspiration increasingly unrealistic: the gap between what trained specialists know and what it is feasible for an educated layperson to understand has grown faster than any educational system can bridge.
An alternative approach, sometimes called "epistocracy," proposes weighting political power in proportion to demonstrated knowledge or expertise. This view is perhaps most rigorously developed by philosopher Jason Brennan, who argues in "Against Democracy" that the dominance of what he calls "hobbits" (politically disengaged citizens) and "hooligans" (those who hold politically motivated, tribally distorted beliefs) undermines the rationality of democratic outcomes. Brennan's proposed solution — various mechanisms for giving more weight to votes cast by better-informed citizens — has attracted significant critical attention.
Critics of epistocracy note that it merely relocates, rather than solves, the problem of legitimate authority. Who decides which knowledge is relevant, and by what standard? Historical examples of governance by "experts" — technocratic regimes and colonial administrations that justified themselves on grounds of superior knowledge — suggest that claimed expertise can mask political interests and systematically exclude the perspectives of those who are governed. The knowledge required for just governance is not merely technical; it includes the lived experiences of citizens whose preferences and vulnerabilities are precisely what policy should address.
Sub-Questions:
The unit of the van der Waals constant '$a$' in the equation $\left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT$ is:
In the van der Waals equation, the term $\dfrac{an^2}{V^2}$ must have units of pressure.
So: $a = \dfrac{P \cdot V^2}{n^2}$
Units of $a = \dfrac{\text{atm} \cdot (\text{dm}^3)^2}{(\text{mol})^2} = \mathbf{\text{atm dm}^6\ \text{mol}^{-2}}$
The constant $b$ has units of dm$^3$ mol$^{-1}$ (it represents excluded molar volume). 'a' corrects for intermolecular attractions.
Maximum power transfer theorem: load resistance should equal:
For maximum power, R_L = R_source (ThΓ©venin resistance).
Let the junction temperature be $T$. In steady state, the heat current through the copper rod equals the sum of currents through brass and steel.
$\frac{K_c A (100 - T)}{L_c} = \frac{K_b A (T - 0)}{L_b} + \frac{K_s A (T - 0)}{L_s}$
$\frac{0.92 \times (100 - T)}{46} = \frac{0.26 \times T}{13} + \frac{0.12 \times T}{12}$
$0.02 (100 - T) = 0.02T + 0.01T \implies 2 - 0.02T = 0.03T \implies 5T = 200 \implies T = 40^\circ\text{C}$.
Rate of heat flow $H = \frac{0.92 \times 4 \times (100 - 40)}{46} = 0.02 \times 4 \times 60 = 4.8 \text{ cal/s}$.
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