U-tube (closed on both ends); multiple gases

Question

The U-tube in the figure is sealed at both ends. It contains a gas A (located in the right arm), another gas B (located in the left arm) and mercury. The heights of mercury in the two arms are as follows:

4 cm on the left side, 7 cm on the right. The density of mercury is

13.6 g/cm^3. If the pressure of A is 1*10^4 dyn/cm^2, what is the pressure of B?

 

answer choices: 

a. 1*10^4 dyn/cm^2

b. 2*10^4 dyn/cm^2

c. 3*10^4 dyn/cm^2

d. 4*10^4 dyn/cm^2

e. 5*10^4 dyn/cm^2

 

I understand that since the mercury doesn't comes up as high in the left arm (where gas B is), that gas B produces more pressure than gas A does, however I'm not sure about where to go from there.

 

Thank you

 

Answer 1

Use this formula:

 

P_B = P_A + ρg(h_A - h_B)

 

P_B = (1 x 10⁴ dyn/cm²) + (13.6 g/cm³)(980 cm/s²)[(7 - 4) cm] = 49,984 dyn/cm² ≅ 5 x 10⁴ dyn/cm²

 

Answer (E) is the best answer.

Answer 2

The difference in height is 3 cm.

3 cm Hg x 13.6 g/cm² = 40.8 g/cm²

40.8 g/cm² x 1 dyn-cm^-2/0.001 g/cm² = 40,800 dyn/cm² = 4x10⁴ dyn/cm²