To determine the mass of a two-phase mixture of mercury in a constant-volume chamber, we need to use the given temperature, quality, and specific volume data for mercury.

Step-by-Step Solution

Step 1: Understand the Problem

Given:

• Volume of the chamber, $V = 1 \, \text{ft}^3$
• Temperature, $T = 1100 \, \text{°R}$
• Quality, $x = 0.9$ (90%)
• The substance is mercury.

We need to find the mass of the mercury mixture in the chamber, $m$ (in lbm).

Step 2: Find the Properties of Mercury at the Given Conditions

The mass of the mixture can be determined using the specific volume relationship:

$v_{\text{mix}} = \frac{V}{m}$

where:

• $v_{\text{mix}}$ is the specific volume of the mixture (in $\text{ft}^3/\text{lbm}$)
• $m$ is the mass (in lbm)

The specific volume of the two-phase mixture is given by:

$v_{\text{mix}} = v_f + x (v_g - v_f)$

where:

• $v_f$ is the specific volume of the saturated liquid mercury at $T = 1100 \, \text{°R}$
• $v_g$ is the specific volume of the saturated vapor mercury at $T = 1100 \, \text{°R}$

Step 3: Obtain Mercury Properties at 1100 °R

We need the values of $v_f$ and $v_g$ for mercury at $T = 1100 \, \text{°R}$. However, these values are typically obtained from mercury property tables or thermodynamic databases. Since we do not have direct access to such a table right now, I will provide a general outline of how to proceed.

Step 4: Calculate the Mass

Once $v_f$ and $v_g$ are known, the specific volume of the mixture $v_{\text{mix}}$ can be calculated using the formula for specific volume given above. Then, the mass of the mixture $m$ can be determined:

$m = \frac{V}{v_{\text{mix}}}$

where:

• $V = 1 \, \text{ft}^3$

Conclusion

To proceed further, you would need the specific volume values of the saturated liquid and vapor mercury at the given temperature of 1100 °R from a reliable thermodynamic property table or database. If you have these values or can access such a source, plug them into the formulas above to compute the mass.

Would you like me to provide an example using hypothetical or estimated values for mercury, or do you have access to the necessary property tables?