BPSC 70th CCE Prelims General Studies · Question 140 of 143

Correct — A, 1.4 kW/m2. The solar constant is the amount of solar energy falling per second on one square metre held perpendicular to the Sun's rays at the top of the Earth's atmosphere, measured at the mean Earth–Sun distance of one astronomical unit. Satellite measurement of total solar irradiance puts it at about 1,361 to 1,367 watts per square metre — that is 1.36 to 1.37 kilowatts per square metre — and Indian school textbooks round that to 1.4 kW/m2, which is the figure this question wants. The same quantity appears in NCERT geography in older units as 1.94 calories per square centimetre per minute; convert it and you land back at roughly 1,353 watts per square metre, so the two forms agree. Of the four options, only 1.4 is within reach of the measured value: 1.2 is about 12 per cent too low and 1.6 and 1.8 are 18 and 32 per cent too high, all far outside anything the instruments record. Two refinements are worth carrying. First, the 'constant' is not perfectly constant — Earth's orbit is elliptical, so the irradiance is a few per cent higher near perihelion in early January than near aphelion in early July, and total solar irradiance also varies by about a tenth of a per cent over the eleven-year solar cycle. Second, this is the value above the atmosphere; by the time sunlight reaches the ground it has been scattered, reflected and absorbed, and clear-sky noon irradiance at the surface is closer to 1 kW/m2 — the very figure solar panels are rated against under standard test conditions.

• (b)1.6 kW/m2 — About 18 per cent above the measured value of roughly 1.36 kW/m2, and outside any variation the Earth's orbit can produce — the perihelion-to-aphelion swing is only a few per cent. It is the nearest overestimate and therefore the option most likely to catch a candidate who remembers only that the figure is 'a bit over one'.
• (c)1.8 kW/m2 — Roughly a third higher than the true value. No standard source, in watts per square metre or in calories per square centimetre per minute, gives anything near this; it is present only to widen the spread of the option set.
• (d)1.2 kW/m2 — Too low for the top of the atmosphere, and tempting for a different reason: it sits between the true solar constant and the roughly 1 kW/m2 of clear-sky sunlight that actually reaches the ground. A candidate who confuses surface irradiance with the extra-terrestrial value drifts towards this number.

Solar energy arriving at the Earth is described by two different numbers, and confusing them is the commonest error in this topic. The solar constant is the extra-terrestrial value: irradiance at the top of the atmosphere, on a surface held at right angles to the beam, at one astronomical unit — about 1,361 watts per square metre, conventionally rounded to 1.4 kW/m2. Surface irradiance is what is left after the atmosphere has taken its share by scattering, cloud reflection and absorption by ozone, water vapour and carbon dioxide, and under clear skies at noon that is around 1 kW/m2. The word 'constant' is historical. Because Earth's orbit is an ellipse, the planet is nearest the Sun in early January and farthest in early July, and the irradiance varies by a few per cent accordingly; superimposed on that is a variation of about a tenth of a per cent across the eleven-year sunspot cycle. Averaged over the whole rotating globe, the energy actually available per square metre of surface is the solar constant divided by four, which is why the Earth's radiation-balance diagrams start from about 340 watts per square metre rather than 1,361.

Two anchors make this question safe without memorising a decimal. The first is the solar-panel anchor: standard test conditions for photovoltaic modules use 1,000 watts per square metre, that is 1 kW/m2, and everyone has met that number. The solar constant must be higher than the surface value, but not by a large multiple, since the atmosphere removes a substantial minority of the incoming energy rather than most of it — so a figure just under one and a half is right and anything approaching double is not. That single comparison removes 1.6 and 1.8 immediately, and 1.2 is suspiciously close to the surface figure. The second anchor is the calorie form that Indian geography textbooks use, 1.94 calories per square centimetre per minute, which converts to about 1.35 kW/m2 and rounds to 1.4. If a question ever offers you both 1.36 and 1.4, take 1.36 as the measured value; where only round figures are offered, as here, 1.4 is the intended textbook answer.

• The solar constant is the solar irradiance at the top of the atmosphere on a surface perpendicular to the rays, at the mean Earth–Sun distance of one astronomical unit
• Satellite measurement of total solar irradiance gives about 1,361 to 1,367 W/m2, that is 1.36 to 1.37 kW/m2, rounded in Indian textbooks to 1.4 kW/m2
• The same value in the older units used in NCERT geography is 1.94 calories per square centimetre per minute, which converts to roughly 1,353 W/m2
• It is not strictly constant: the elliptical orbit makes irradiance a few per cent higher near perihelion in early January than near aphelion in early July, and total solar irradiance varies about 0.1 per cent over the eleven-year solar cycle
• Clear-sky irradiance at the Earth's surface is about 1 kW/m2, which is the standard test condition used to rate solar photovoltaic panels
• Averaged over the whole globe, incoming solar energy is the solar constant divided by four, roughly 340 W/m2, the starting point of the Earth's radiation-balance diagram

• Quoting the surface value of about 1 kW/m2 when the question asks for the solar constant at the top of the atmosphere
• Treating the solar constant as literally invariant; it changes with the Earth–Sun distance and slightly with the solar cycle
• Mixing up the perpendicular-surface value with the globally averaged figure, which is one-quarter of it

BPSC asks physical geography as a single remembered number with four near-neighbours as options, so the safeguard is to hold one anchor value you can reason from rather than four decimals you might swap. UPSC does not ask the solar constant outright; it asks what the number is for — the heat budget, why carbon dioxide traps the outgoing infrared, how clouds change the balance — so the same fact has to be understood as part of an energy accounting rather than memorised.

• practice — not a real PYQ

  The solar constant is measured at

  • (a)The Earth's surface at the Equator
  • (b)The top of the Earth's atmosphere, at the mean Earth–Sun distance
  • (c)The surface of the Sun
  • (d)The tropopause over the poles

  Answer(b) The top of the Earth's atmosphere, at the mean Earth–Sun distance — on a surface held perpendicular to the rays; by the time sunlight reaches the ground the value has fallen to roughly 1 kW/m2.

• practice — not a real PYQ

  The Earth is nearest to the Sun (perihelion) in which month ?

  • (a)January
  • (b)April
  • (c)July
  • (d)October

  Answer(a) January — the Earth reaches perihelion in early January and aphelion in early July, which is why the solar constant varies by a few per cent through the year.