Question 85: Thermodynamics & KTG

Question

Equal volumes of two gases, having their
densities in the ratio of 1 : 16 exert equal
pressures on the walls of two containers. The
ratio of their rms velocities $$\left(\frac{c_1}{c_2}\right)$$

Accepted Answer

Densities ratio of two gases,
$$ho_1:ho_2=1:16$$
$$\Rightarrow \quad \frac{ho_1}{ho_2}=\frac{1}{16}$$
Since, pressure of both gases are equal.
$$	herefore  p_1  =p_2$$
$$\frac{1}{3} ho_1 c_1^2 =\frac{1}{2} ho_2 c_2^2$$
$$\Rightarrow \frac{c_1^2}{c_2^2} =\frac{ho_2}{ho_1}=\frac{16}{1}$$
$$=\left(\frac{4}{1}ight)^2$$
$$\Rightarrow \frac{c_1}{c_2}  =\frac{4}{1}$$
$$\Rightarrow  c_1: c_2  =4: 1$$

Answer

1 : 8

Answer

8 : 1

Answer

1 : 4

Answer

4 : 1

Thermodynamics & KTG

Equal volumes of two gases, having their densities in the ratio of 1 : 16 exert equal pressures on the walls of two containers. The ratio of their rms velocities $\left(\frac{c_1}{c_2}\right)

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