Question

Problem twelve: A cylinder contains two samples of different ideal gases. A piston separating the two gaves is free to move without friction. Each gas occupies half of the cylinder, but there are twice as many molecules on the left side of the piston as on the right, and the absolute temperature is twice as large for the gas on the right side as for the gas on the left Piston 00 6 moles 3 moles 400 K 800 K Is the pressure in the gas on the left side (i) greater than, (ii) less than or dil) equal to the pressure in the gas on the right side? Explain your reasoning.

Answer 1

Using the Ideal gas equation for each side of the cylinder and know that the piston is in the half of the cylinder, indicates that gases occupy the same volume, then.

PV nRT

$P_1V=n_1RT_1$

$P_2V=n_2RT_2$

combine both ecuations, we have that

$\frac{n_1T_1}{P_1}=\frac{n_2T_2}{P_2}$

substituting the values

$\frac{6 moles\times400K}{P_1}=\frac{3 moles\times800 K}{P_2}\Rightarrow \frac{2400}{P_1}=\frac{2400}{P_2}$

Therefore, the two gases must have the same pressure for the equation of state to be satisfied.