Question 555: Thermodynamics & KTG

Question

1 mole of rigid diatomic gas performs a work of $${Q \over 5}$$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $${xR \over 8}$$. The value of x is _________. [R = universal gas constant]

Accepted Answer

From thermodynamics law:
$$Q = \Delta U + W$$
$$Q = \Delta U + {Q \over 5}$$
$$\Delta U = {{4Q} \over 5}$$
$$n{C_v}\Delta T = {4 \over 5}nC\Delta T$$
$${5 \over 4}{C_v} = C$$
$$C = {5 \over 4}\left( {{f \over 2}} \right)R = {5 \over 4}\left( {{5 \over 2}} \right)R$$
$$C = {{25} \over 8}R$$
$$X = 25$$

Thermodynamics & KTG

1 mole of rigid diatomic gas performs a work of ${Q \over 5} when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is {xR \over 8}$. The value of x is _________. [R = universal gas constant]

Integer / Numeric Answer Type