# 1 kg of atomic material (i.e., uranium) can produced as much energy as produced by burning _________.

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UPPCL JE Electrical 7 Sept 2021 Official Paper (Shift 2)
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1. 3,000 tonnes of high grade coal.
2. 3,300 tonnes of high grade coal
3. 300 tonnes of high grade coal.
4. 30,000 tonnes of high grade coal

Option 1 : 3,000 tonnes of high grade coal.

## Detailed Solution

Concept:

Mass–energy equivalence: The equivalence of mass and energy is a consequence of Einstein’s theory of special relativity.

The mass can be converted into energy and visa-versa.

​The mass-energy equivalence can be given by:

E = m c2

Where E = Energy, m = Mass, c = Speed of light = 3 × 108 m/s

Calorific value of fuels: The calorific value (CV) or heat value of solid or liquid fuel is defined as the amount of heat given out by the complete combustion of 1 kg of fuel

• It is expressed in terms of kJ/kg.
• The calorific value of gaseous fuel is expressed in terms of kJ/m3 at a specified temperature and pressure.

Calorific value of high grade coal is 30 MJ/kg

Also, 1 tonne = 1000 kg

Calculation:

Given:

m = 1 kg, c = 3 × 108 m/s

Using E = m c2

E = 1 × (3 × 108 )2

E = 9 × 1016 J

E = 9 × 1010 MJ

1 kg of coal can produce 30 MJ of energy.

Mass of coal(M) required to produce 9 × 1010 MJ = $$\frac {9\times 10^{10}}{30} = 3\times 10^9$$

M = 3000 tonnes
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