Using the ESRT to find the Relative Humidity - Relative Humidity is the extent to which air is saturated with water vapor. - Relative humidity is the ratio of the amount of water vapor in the air to the maximum amount of water vapor that can be present could be present in the air at that temperature. - Relative Humidity is expressed as a percent (\%). - Evaporation is a cooling process. - Therefore, the wet-bulb temperature is always lower than the dry-bulb temperature EXCEPT when relative humidity is $$ 100 \% $$. Then the wet-bulb temperature is equal to the dry-bulb temperature. Practice Problems: 1. Dry-bulb Temperature: $$ \mathbf{2 0}^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 7^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 2. Dry-bulb Temperature: $$ 8^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 5^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 3. Dry-bulb Temperature: $$ \mathbf{2 4}^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ \mathbf{2 2}^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 4. Dry-bulb Temperature: $$ \mathbf{2 0}^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 7^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 5. Dry-bulb Temperature: $$ 10^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 1^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 6. Dry-bulb Temperature: $$ 6^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 5^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 7. Dry-bulb Temperature: $$ 30^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ 23^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Let's try some more complex examples... 8. Dry-bulb Temperature: $$ -14^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ -15^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: $$ \qquad $$ \% 9. Dry-bulb Temperature: $$ -2^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ \qquad $$ $$ { }^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: 58 \% 10. Dry-bulb Temperature: $$ -8^{\circ} \mathrm{C} $$ Wet-bulb Temperature: $$ \qquad $$ $$ { }^{\circ} \mathrm{C} $$ Difference between wet \& dry bulb temperatures: $$ \qquad $$ Relative Humidity: 41 \%

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To find the relative humidity and the difference between the wet-bulb and dry-bulb temperatures for the given problems, we can follow these steps:

1. **Calculate the difference between the wet-bulb and dry-bulb temperatures**:
   $$
   \text{Difference} = \text{Dry-bulb Temperature} - \text{Wet-bulb Temperature}
   $$

2. **Use the difference to find the relative humidity**. The relative humidity can be estimated using a formula that relates the dry-bulb temperature, wet-bulb temperature, and relative humidity. However, for simplicity, we can use a table or a calculator that provides relative humidity based on these temperatures.

Let's solve each problem step by step.

### Problem 1
- Dry-bulb Temperature: $$ 20^{\circ}C $$
- Wet-bulb Temperature: $$ 7^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 20 - 7 = 13^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Using a psychrometric chart or calculator, we find that the relative humidity is approximately $$ 30\% $$.

### Problem 2
- Dry-bulb Temperature: $$ 8^{\circ}C $$
- Wet-bulb Temperature: $$ 5^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 8 - 5 = 3^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 60\% $$.

### Problem 3
- Dry-bulb Temperature: $$ 24^{\circ}C $$
- Wet-bulb Temperature: $$ 22^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 24 - 22 = 2^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 90\% $$.

### Problem 4
- Dry-bulb Temperature: $$ 20^{\circ}C $$
- Wet-bulb Temperature: $$ 7^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 20 - 7 = 13^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 30\% $$.

### Problem 5
- Dry-bulb Temperature: $$ 10^{\circ}C $$
- Wet-bulb Temperature: $$ 1^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 10 - 1 = 9^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 30\% $$.

### Problem 6
- Dry-bulb Temperature: $$ 6^{\circ}C $$
- Wet-bulb Temperature: $$ 5^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 6 - 5 = 1^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 90\% $$.

### Problem 7
- Dry-bulb Temperature: $$ 30^{\circ}C $$
- Wet-bulb Temperature: $$ 23^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = 30 - 23 = 7^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 60\% $$.

### Problem 8
- Dry-bulb Temperature: $$ -14^{\circ}C $$
- Wet-bulb Temperature: $$ -15^{\circ}C $$

**Step 1: Calculate the difference**
$$
\text{Difference} = -14 - (-15) = 1^{\circ}C
$$

**Step 2: Estimate Relative Humidity**
Relative humidity is approximately $$ 90\% $$.

### Problem 9
- Dry-bulb Temperature: $$ -2^{\circ}C $$
- Wet-bulb Temperature: $$ \text{unknown} $$

**Given Relative Humidity: $$ 58\% $$**

**Step 1: Use relative humidity to find wet-bulb temperature.**
Using a psychrometric chart or calculator, we find that the wet-bulb temperature is approximately $$ -4^{\circ}C $$.

**Step 2: Calculate the difference**
$$
\text{Difference} = -2 - (-4) = 2^{\circ}C
$$

### Problem 10
- Dry-bulb Temperature: $$ -8^{\circ}C $$
- Wet-bulb Temperature: $$ \text{unknown} $$

**Given Relative Humidity: $$ 41\% $$**

**Step 1: Use relative humidity to find wet-bulb temperature.**
Using a psychrometric chart or calculator, we find that the wet-bulb temperature is approximately $$ -10^{\circ}C $$.

**Step 2: Calculate the difference**
$$
\text{Difference} = -8 - (-10) = 2^{\circ}C
$$

### Summary of Results
1. Difference: $$ 13^{\circ}C $$, Relative Humidity: $$ 30\% $$
2. Difference: $$ 3^{\circ}C $$, Relative Humidity: $$ 60\% $$
3. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 90\% $$
4. Difference: $$ 13^{\circ}C $$, Relative Humidity: $$ 30\% $$
5. Difference: $$ 9^{\circ}C $$, Relative Humidity: $$ 30\% $$
6. Difference: $$ 1^{\circ}C $$, Relative Humidity: $$ 90\% $$
7. Difference: $$ 7^{\circ}C $$, Relative Humidity: $$ 60\% $$
8. Difference: $$ 1^{\circ}C $$, Relative Humidity: $$ 90\% $$
9. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 58\% $$
10. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 41\% $$
Here are the differences and relative humidities for each problem: 1. Difference: $$ 13^{\circ}C $$, Relative Humidity: $$ 30\% $$ 2. Difference: $$ 3^{\circ}C $$, Relative Humidity: $$ 60\% $$ 3. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 90\% $$ 4. Difference: $$ 13^{\circ}C $$, Relative Humidity: $$ 30\% $$ 5. Difference: $$ 9^{\circ}C $$, Relative Humidity: $$ 30\% $$ 6. Difference: $$ 1^{\circ}C $$, Relative Humidity: $$ 90\% $$ 7. Difference: $$ 7^{\circ}C $$, Relative Humidity: $$ 60\% $$ 8. Difference: $$ 1^{\circ}C $$, Relative Humidity: $$ 90\% $$ 9. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 58\% $$ 10. Difference: $$ 2^{\circ}C $$, Relative Humidity: $$ 41\% $$

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