Which one of following gases possesses largest internal energy

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11.Thermodynamics

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Which one of the following gases possesses the largest internal energy

A

$2$ moles of helium occupying $1{m^3}$at $300 K$

B

$56 kg$ of nitrogen at $10^7N{m^{ - 2}}$ and $300 K$

C

$8$ grams of oxygen at $8 \,atm$ and $300 K$

D

$6 \times {10^{26}}$ molecules of argon occupying $40{m^3}$ at $ 900 K$

Solution

(b) $\Delta U = \mu {C_V}\Delta T = \frac{m}{M}{C_V}\Delta T = \frac{N}{{{N_A}}}{C_V}\Delta T$

==>${(\Delta U)_N} = \frac{{56 \times {{10}^3}}}{{14}} \times \frac{5}{2}R \times 300$

and ${(\Delta U)_A} = \frac{{6 \times {{10}^{26}}}}{{6 \times {{10}^{23}}}} \times \frac{3}{2}R \times 900$

$\Rightarrow {(\Delta U)_N} > {(\Delta U)_A}$

Standard 11

Physics

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