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The useful energy available by burning $1g$ coal is $2kcal$ . The cost of producing $1Wh$ energy is ($1kg{\text{ }}coal = 21paise)$?
(A) $9 paise$
(B) $18 paise$
(C) $4.5 paise$
(D) $36 paise$

Last updated date: 13th Jun 2024
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Hint: We first have to check for unit consistency, energy is given in $kcal$ as well as $joules$ and $kilowatt{\text{ }}hour$ So we first convert Everything to $joules$. In the question we are given how much coal is needed for $2kcal$ now we convert the $2kcal$ to $joules$. Then convert $1Wh$ energy to $joules$ then find out how much coal is needed for $2kcal$. Using the weight of coal found we find the price using the amount of coal price from the question. Unit consistency is very important.

Complete step by step solution:
Firstly converting all the given units of energies to joules,
$2kcal = 8400 joules $
$1kWh = 3.6 \times {10^6} joules $
 From the question we know that $2kcal = 8400joules$ requires $1gm$ coal, so for $1kwh = 3.6 \times {10^6} joules$ require ,
$\dfrac{{3.6 \times {{10}^6}}}{{8400}} \times 1 = \dfrac{{3000}}{7}gms = \dfrac{3}{7}kg$
We also know from the question that $1kg$ coal costs $21 paise$ so $\dfrac{3}{7}kg$ will cost,
$\dfrac{3}{7} \times 21 = 9 paise$
Hence the cost of producing $1kwh = 3.6 \times {10^6} joules$ of useful energy is $9paise$.

The correct answer is option (A), $9paise$.

Additional information: Coal-fired plants produce electricity by burning coal in a boiler to produce steam. The steam produced, under tremendous pressure, flows into a turbine, which spins a generator to create electricity. The steam is then cooled, condensed back into the water, and returned to the boiler to start the process over.

Note: This is a problem that needs basic math knowledge, the only tricky part of the question is to convert all the units of energy to a single common unit and solve for the weight of coal, and finding the cost from the cost in the question given data. The amount of energy released by one kilogram of coal during combustion is $3 \times {10^7} joules$.