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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3td212

An ideal gas has $C_{P} = 4.5 R$ per mole, with $R = 8.314 J mo l^{- 1} K^{- 1}$ . Select all correct statements.

A $C_{V} \approx 29.1 J mo l^{- 1} K^{- 1}$
B $γ = 1.40$
CThe gas cannot be monatomic
DHeating $2 mol$ by $100 K$ at constant volume needs about $5.82 kJ$

Answer: A, C, D

C_{V} = C_{P} - R = 3.5 R = 29.10 J mo l^{- 1} K^{- 1}

. Then

γ = 4.5/3.5 = 1.286

, not

1.40

, so statement 2 is false. A monatomic gas has

C_{P} = 2.5 R

, so this gas cannot be monatomic.

q_{V} = 2 \times 29.10 \times 100 = 5820 J = 5.82 kJ

.

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