liquid a is known to have a higher viscosity and higher vapor pressure than liquid b. use these facts to predict the result of each experiment in the table below, if you can. | experiment | predicted outcome | | --- | --- | | liquid a and liquid b are each pumped through tubes with an inside diameter of 13.0 mm, and the pressures $p_a$ and $p_b$ needed to produce a steady flow of 3.5 ml/s are measured. | $p_a$ will be greater than $p_b$
$p_a$ will be less than $p_b$
$p_a$ will be equal to $p_b$
its impossible to predict whether $p_a$ or $p_b$ will be greater without more information. | | 15.0 ml of liquid a are poured into a beaker. 15.0 ml of liquid b are poured into another beaker. after 90 minutes have passed, the volumes $v_a$ and $v_b$ of liquid in each beaker are measured. | $v_a$ will be greater than $v_b$
$v_a$ will be less than $v_b$
$v_a$ will be equal to $v_b$
its impossible to predict whether $v_a$ or $v_b$ will be greater without more information. |

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# Explanation:
## Experiment 1:
### Step1: Viscosity and flow - pressure relationship
Viscosity ($\eta$) is related to the pressure ($P$) needed to maintain a flow rate ($Q$) through a tube of radius $r$ and length $L$ by the Hagen - Poiseuille equation $Q=\frac{\pi r^{4}P}{8\eta L}$. For a given $Q$, $r$, and $L$, $P = \frac{8\eta LQ}{\pi r^{4}}$. Since Liquid A has a higher viscosity ($\eta_A>\eta_B$), and other factors ($Q$, $r$, $L$) are the same (same tube diameter means same $r$, same flow rate $Q$), the pressure $P$ is directly proportional to viscosity.

### Step2: Compare $P_A$ and $P_B$
From $P = \frac{8\eta LQ}{\pi r^{4}}$, when $\eta_A>\eta_B$, $P_A$ (pressure for Liquid A) will be greater than $P_B$ (pressure for Liquid B).

## Experiment 2:
### Step1: Vapor pressure and evaporation
Vapor pressure ($P_{vap}$) is a measure of the tendency of a liquid to evaporate. A liquid with a higher vapor pressure evaporates more readily. Liquid A has a higher vapor pressure ($P_{vap,A}>P_{vap,B}$).

### Step2: Compare $V_A$ and $V_B$
The initial volumes ($V_{0,A} = V_{0,B}=15.0\space mL$) are the same. After 90 minutes, the volume of the liquid remaining $V = V_0 - \Delta V$, where $\Delta V$ is the volume of liquid that has evaporated. Since $P_{vap,A}>P_{vap,B}$, Liquid A evaporates more ($\Delta V_A>\Delta V_B$), so $V_A=V_{0,A}-\Delta V_A$ and $V_B = V_{0,B}-\Delta V_B$, and $V_A$ will be less than $V_B$.

# Answer:
- For the first experiment: $P_A$ will be greater than $P_B$
- For the second experiment: $V_A$ will be less than $V_B$

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QUESTION IMAGE

Question

Explanation:

Experiment 1:

Step1: Viscosity and flow - pressure relationship

Step2: Compare \(P_A\) and \(P_B\)

Experiment 2:

Step1: Vapor pressure and evaporation

Step2: Compare \(V_A\) and \(V_B\)

Answer: