SATHEE: Heat and Thermodynamics 4 Question 11

Heat and Thermodynamics 4 Question 11

13. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature $T$ . Considering only translational and rotational modes, the total internal energy of the system is

(2019 Main, 11 Jan I)

(a) $12 R T$

(b) $15 R T$

(d) $4 R T$

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Solution:

Internal energy of a gas with $f$ degree of freedom is

$U = \frac{n f R T}{2}$ , where $n$ is the number of moles.

Internal energy due to $O_{2}$ gas which is a diatomic gas is

$U_{1} = \frac{n_{1} f_{1} R T}{2} = 3 \times \frac{5}{2} R T$

$(∵ n_{1} = 3$ moles, degree of freedom for a diatomic gas $f_{1} = 5$ )

Internal energy due to Ar gas which is a monoatomic gas is

$U_{2} = \frac{n_{2} f_{2} R T}{2} = 5 \times \frac{3}{2} R T$

$(∵ n_{2} = 5$ moles, degree of freedom for a monoatomic gas $f_{2} = 3$ )

$∴$ Total internal energy $= U_{1} + U_{2}$

$\Rightarrow U = 15 R T$

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Heat and Thermodynamics 4 Question 11

13. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

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13. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature $T$ . Considering only translational and rotational modes, the total internal energy of the system is