Question

A container is filled with $20$ moles of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to gas, temperature remains constant but $8$ moles dissociate into atoms. Heat energy given to gas is

• A. $4RT$
• B. $6RT$
• C. $3RT$
• D. $5RT$

Answer 1

The correct option is A $4RT$

Average Energy of 20 moles of diatomic gas $=n\times \frac{5}{2}\times RT$$=20\times \frac{5}{2}\times RT=50RT$

Average Energy of $12$ $moles$ of diatomic gas $+16$ $moles$ of monoatomic gas $(8$ $moles\rightleftharpoons 16$ $moles)$

$=12\times \frac{5}{2}\times RT$$+16\times \frac{3}{2}\times RT=54RT$

Heat supplied to the gas $=54RT-50RT=4RT$