N moles of a diatomic gas in a cylinder are a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The initial internal energy of $N$ moles of diatomic gas is given by $U_i = N \left( \frac{5}{2} RT \right)$.When $n$ moles of diatomic gas dissoc

Vedclass · Accepted Answer

$\frac{1}{2}nRT$

Vedclass · Answer

(A) The initial internal energy of $N$ moles of diatomic gas is given by $U_i = N \left( \frac{5}{2} RT \right)$.When $n$ moles of diatomic gas dissociate into monoatomic gas,each diatomic molecule splits into two monoatomic atoms. Thus,$n$ moles of diatomic gas produce $2n$ moles of monoatomic gas.The remaining amount of diatomic gas is $(N-n)$ moles.The final internal energy $U_f$ is the sum of the energy of the monoatomic gas and the remaining diatomic gas:$U_f = (2n) \left( \frac{3}{2} RT \right) + (N-n) \left( \frac{5}{2} RT \right)$.$U_f = 3nRT + \frac{5}{2}NRT - \frac{5}{2}nRT = \frac{5}{2}NRT + \frac{1}{2}nRT$.The change in internal energy $\Delta U = U_f - U_i$ is:$\Delta U = \left( \frac{5}{2}NRT + \frac{1}{2}nRT \right) - \left( \frac{5}{2}NRT \right) = \frac{1}{2}nRT$.

$N$ moles of a diatomic gas in a cylinder are at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?

Similar Questions

$A$ rigid diatomic gas having molar mass $M$ is contained in an insulated container. The container is moving with velocity $V$. If it is stopped suddenly, the change in temperature is ($R$ - gas constant).

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points $(V_{0}, T_{0})$ and $(2 V_{0}, 3 T_{0})$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_{0}, T_{0})$?

The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$

According to the kinetic theory of gases,when two molecules of a gas collide with each other,then:

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module