Question 885: Thermodynamics & KTG

Question

According to kinetic theory of gases, which one of the following statements is wrong?

Accepted Answer

According to Wien's law, $$\lambda_{\mathrm{m}} \mathrm{T}=$$ constant (b)
$$	herefore \mathrm{T}=\frac{\mathrm{b}}{\lambda_{\mathrm{m}}}\quad 	ext{..... (1)}$$
and from Stefan's law, $$\mathrm{Q}=\sigma \mathrm{AT}^4\quad 	ext{.... (2)}$$
For the disc, area $$(\mathrm{A})=\pi \mathrm{r}^2$$
$$	herefore$$ From (1) and (2),
$$\mathrm{Q}=\sigma \cdot \pi \mathrm{r}^2 \cdot \frac{\mathrm{b}^4}{\lambda_{\mathrm{m}}^4}=\frac{\mathrm{Kr}^2}{(\lambda \mathrm{m})^4}$$
where $$\mathrm{K}=\pi \sigma \mathrm{b}^4$$ is a constant
$$\mathrm{Q}$$ is the quantity of heat radiated per second or power.
Hence $$\mathrm{P}_{\mathrm{x}}, \mathrm{P}_{\mathrm{y}}$$ and $$\mathrm{P}_{\mathrm{z}}$$ are the powers of $$\mathrm{x}, \mathrm{y}, \mathrm{z}$$.
For $$\mathrm{x}$$ we have $$\mathrm{r}_1=2 \mathrm{~m}$$ and $$\lambda_1=300 \mathrm{~nm}$$
For $$y$$, we have $$r_2=3 \mathrm{~m}$$ and $$\lambda_2=400 \mathrm{~nm}$$
and For $$\mathrm{z}$$, we have $$\mathrm{r}_3=6 \mathrm{~m}$$ and $$\lambda_3=500 \mathrm{~nm}$$
$$\begin{aligned}
	herefore \mathrm{P}_{\mathrm{x}} & \propto \frac{\mathrm{r}_1^2}{\lambda_1^4} 	ext { or } \frac{2^2}{\left(3 	imes 10^{-7}ight)^4} 	ext { or } \frac{4 	imes 10^{+28}}{81} \
\mathrm{P}_{\mathrm{y}} & \propto \frac{\mathrm{r}_2^2}{\lambda_2^4} 	ext { or } \frac{9 	imes 10^{+28}}{256} \
\mathrm{P}_{\mathrm{z}} & \propto \frac{\mathrm{r}_3^2}{\lambda_3^4} 	ext { or } \frac{36 	imes 10^{28}}{625}
\end{aligned}$$
But $$\frac{4}{81}=0.049, \frac{9}{250}=0.035$$ and $$\frac{36}{625}=0.0576$$
$$	herefore \mathbf{P}_{\mathrm{z}}$$ is maximum.

Answer

All the molecules of a gas are identical.

Answer

Collisions between the molecules of a gas and that of the molecules with the walls of the container are perfectly elastic.

Answer

The molecules do not exert appreciable force on one another except during collision.

Answer

The pressure exerted by a gas is due to the collision between the molecules of the gas.

Thermodynamics & KTG

According to kinetic theory of gases, which one of the following statements is wrong?

Choose the correct answer: