e value of $ Q $.

Initially, the gas has 4 moles of an ideal diatomic gas. When supplied with heat, 2 moles dissociate into monoatomic gas, effectively converting 2 moles of diatomic gas into 4 moles of monoatomic gas.

Degrees of Freedom

Diatomic gas: $ f = 5 $

Monoatomic gas: $ f = 3 $

Internal Energy Calculation

The internal energy $ E $ for gas is given by:

$ E = n \times \frac{f}{2} \times RT $

Where $ n $ is the number of moles, $ f $ is the degree of freedom, $ R $ is the universal gas constant, and $ T $ is the temperature.

Initial Internal Energy $ E_i $

For 4 moles of diatomic gas:

$ E_i = 4 \times \frac{5}{2} \times RT = 10RT $

Final Internal Energy $ E_f $

After dissociation, we have:

2 moles of diatomic gas:

$ 2 \times \frac{5}{2} \times RT = 5RT $

4 moles of monoatomic gas:

$ 4 \times \frac{3}{2} \times RT = 6RT $

Total final internal energy:

$ E_f = 5RT + 6RT = 11RT $

Change in Internal Energy

The change in internal energy is:

$ \Delta E = E_f - E_i = 11RT - 10RT = RT $

Thus, the value of $ Q $ required to maintain constant temperature during the dissociation process is $ RT $.

Heat And Thermodynamics

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