Heat $$Q=32RT$$ is supplied to $$4$$ moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms $$is_________$$.

Question

Heat $$Q=32RT$$ is supplied to $$4$$ moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms $$is_________$$.

Infinity Learn · Accepted Answer

Let x moles of diatomic gas be associated. x moles of diatomic gas become 2x moles of a monatomic gas after dissociation. Internal energy of n moles of an ideal gas

$= \frac{3}{2} nRT$ for monatomic gas

Internal energy of n moles of an ideal gas

$= \frac{5}{2} nRT$ (for diatomic gas)

So. [Internal energy of 2x moles of a monatomic gas + internal energy of (4 - x) moles of a diatomic gas = internal energy of 4 moles of a diatomic gas

$= \frac{3}{2} RT$ (given)

$\Rightarrow (2 x) (\frac{3 RT}{2}) + (4 - x) (\frac{5}{2} RT) - (4) (\frac{5}{2} RT) = \frac{3}{2} RT$

On solving, x = 3 moles.

Specific heat and degrees of freedom

Remember concepts with our Masterclasses.

Heat $Q = \frac{3}{2} RT$ is supplied to 4 moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms is_________.

Ready to Test Your Skills?

free study material

Specific heat and degrees of freedom

Remember concepts with our Masterclasses.

Heat Q=32RT is supplied to 4 moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms is_________.

Ready to Test Your Skills?

free study material

Heat $Q = \frac{3}{2} RT$ is supplied to 4 moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms is_________.