An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. T

1.	An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. The energy of the gas is1. 6 × 104 J2. 108 J3. 9 × 106 J4. 3 × 102 J
Answer» Correct Answer - Option 3 : 9 × 10⁶ J Concept: Internal energy of ‘n’ moles of a gas with degree of freedom f (=3 for an ideal gas), at temperature T is given as: \({\rm{E}} = \frac{{\rm{f}}}{2}{\rm{nRT}} = \frac{3}{2}{\rm{nRT}}\) So, for an ideal gas, the internal energy is given as: \({\rm{E}} = \frac{3}{2}{\rm{nRT}}\) ∵ [pV = nRT] \({\rm{E}} = \frac{3}{2}pV\) Where, p = Pressure of the gas V = Volume of the gas Calculation: On substituting the given values, \({\rm{E}} = \frac{3}{2} \times 3 \times {10^6} \times 2\) E = 9 × 10⁶ J

An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. The energy of the gas is1. 6 × 104 J2. 108 J3. 9 × 106 J4. 3 × 102 J

Answer» Correct Answer - Option 3 : 9 × 10⁶ J

Concept:

Internal energy of ‘n’ moles of a gas with degree of freedom f (=3 for an ideal gas), at temperature T is given as:

\({\rm{E}} = \frac{{\rm{f}}}{2}{\rm{nRT}} = \frac{3}{2}{\rm{nRT}}\)

So, for an ideal gas, the internal energy is given as:

\({\rm{E}} = \frac{3}{2}{\rm{nRT}}\)

∵ [pV = nRT]

\({\rm{E}} = \frac{3}{2}pV\)

Where,

p = Pressure of the gas

V = Volume of the gas

Calculation:

On substituting the given values,

\({\rm{E}} = \frac{3}{2} \times 3 \times {10^6} \times 2\)

E = 9 × 10⁶ J

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