# Sensible Heat Formula

The perceptible heat is referred to as **“sensible heat.”** The energy that moves from one system to another alters the temperature instead of changing its phase. Instead of melting ice, for instance, it warms the water. In other words, it’s the heat you experience when you’re over a fire or outside on a hot day. Sensible heat is contrasted with latent heat since the two are fundamentally dissimilar (the heat required to shift from one form of matter to another without changing temperature).

Condensation occurs in a cooling system when latent heat is released and the refrigerant (cooling liquid) changes temperature as a result of sensible heat. While the latent heat capacity is used to explain the ability to remove moisture from the air, the sensible heat capacity is used to explain the ability to lower the temperature.

**What is Sensible Heat?**

The energy that is discharged into the atmosphere or absorbed is known as sensible heat. Only the shift in the temperature of a gas or material, not the phase shift causes sensible heat to be of concern. The phase transition between solid, liquid, and gas is relevant to latent heat. The sensible heat formula is utilized to calculate airflow in an electric furnace.

For instance, if you start heating a container of water, you can feel the variations in temperature by dipping your fingers in the water. This procedure is referred to as sensible heating because you can feel the temperature grow over time.

The SI system uses the** joule (J)** as the measure of sensible heat, while the FPS system uses **Btu.**

**Formula for Sensible Heat**

The formula required for calculating the Sensible Heat is

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})where,

Qis External heat gain in Btu/h_{sensible}1.10is the product of the air’s heat capacity (0.018 Btu/oF)Cis airflow rate moving in from outside_{fm}tis Outside temperature_{o }tis the Inside temperature_{i }

## Example of Sensible Heat

Examples, where the concept of Sensible Heat is observed, are:

- The most common example we have seen of sensible heat is when we get out of our house in the summer, or, we can say, on a hot sunny day, we feel something different from the winter or a cold day. This is because of the change in temperature in the surrounding area.
- When we go camping and do bonfires, we observe the sensation of heat when we get close to the bonfire, which is sensible heat. This is because of the change in the temperature of items.
- When we boil normal water in a pan by using a gas stove, we light the fire first, and then the process starts as the fire continues to heat the water pan and the water’s temperature starts to increase. Sensible heat is what causes the water’s temperature to change (from room temperature to boiling point).

## Solved Examples on Sensible Heat Formula

**Example 1: When the indoor air temperature (t _{i}) is 68^{o} F and the outside air temperature (t_{o}) is 78^{o} F, determine the sensible heat gain with a ventilation flow rate of 20,000 C_{fm}.**

**Solution:**

We have,

C_{fm}= 20,000

t_{o}= 78^{o}F

t_{i}= 68^{o}F

Using the formula of sensible heat

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

Q_{sensible}= 1.10 × 20000 × (78 – 68)

= 1.10 × 20000 × 10

Q_{sensible}= 220,000 Btu/h

Therefore, the sensible heat gain is 220,000 Btu/h

**Example 2: When the indoor air temperature (t _{I}) is 54^{o} F and the outside air temperature (to) is 84^{o} F, determine the sensible heat gain with a ventilation flow rate of 10,000 C_{fm.}**

**Solution:**

We have,

C_{fm}= 10,000

t_{o}= 84oF

t_{i}= 54oF

Using the formula of sensible heat

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

Q_{sensible}= 1.10 × 10000 × (84 – 54)

= 1.10 × 10000 × 30

Q_{sensible}= 330,000 Btu/h

Therefore, the sensible heat gain is 330,000 Btu/h.

**Example 3: When the indoor air temperature (t _{i}) is 20^{o} F and the outside air temperature (t_{o}) is 40^{o}F, determine the sensible heat gain with a ventilation flow rate of 20,000 C_{fm}.**

**Solution:**

We have,

C_{fm}= 10,000

t_{o}= 40^{o}F

t_{i}= 20^{o}F

Using the formula of sensible heat

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

Q_{sensible}= 1.10 × 20000 × (40 – 20)

= 1.10 × 20000 × 20

Q_{sensible}= 440,000 Btu/h

Therefore, the sensible heat gain is 440,000 Btu/h.

**Example 4: When the indoor air temperature (t _{i}) is 32^{o}F and the outside air temperature (t_{o}) is 42^{o}F, determine the sensible heat gain with a ventilation flow rate of 10,000 C_{fm}.**

**Solution:**

We have,

C_{fm}= 10,000

t_{o}= 42^{o}F

t_{i}= 32^{o}F

Using the formula of sensible heat

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

Q_{sensible}= 1.10 × 10000 × (42 – 32)

= 1.10 × 10000 × 10

Q_{sensible}= 110,000 Btu/h

Therefore, the sensible heat gain is 110,000 Btu/h.

**Example 5: When the indoor air temperature (t _{i}) is 66^{o}F and the outside air temperature (t_{o}) is 72^{o}F, determine the sensible heat gain with a ventilation flow rate of 30,000 C_{fm}.**

**Solution:**

We have,

C_{fm}= 10,000

t_{o }= 72°F

t_{i }= 66°F

Using the formula of sensible heat

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

Q_{sensible }= 1.10 × 30000 × (72 – 66)

= 1.10 × 30000 × 6

Q_{sensible }= 198,000 Btu/h

Therefore, the sensible heat gain is 198,000 Btu/h.

**FAQs on Sensible Heat Formula**

**Question 1: Define sensible heat with an example.**

**Answer:**

The energy that is discharged into the atmosphere or absorbed is known as sensible heat.

Example:If you start heating a container of water, you can feel the variations in temperature by dipping your fingers in the water. This procedure is referred to as sensible heating because you can feel the temperature grow over time.

**Question 2: What formula is used for calculating heat gain?**

**Answer: **

The formula used for calculating heat gain is

Q_{sensible}= 1.10 × C_{fm}× (t_{o}-t_{i})

**Question 3: Write the difference between sensible and latent heat.**

**Answer:**

Sensible heat differs from latent heat in that it causes a change in temperature, either upward or downward the temperature change will be constant and unchanging in latent heat.

**Question 4: When do we check the fever of a patient who has a fever of at least 100 ^{o}C using a thermometer? Is this an example of sensible heat or latent heat?**

**Answer:**

Yes, this is an example of sensible heat, as the first thermometer is at 0

^{o}C, but when we use it on a patient, the temperature will rise, and this is because of the high temperature of the body.

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