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1102-A: Heat Formula 1

• Topic Cluster: Thermodynamics
• Topic: Heat Transfer and Temperature: Mathematical
• Objective: Determine the heat energy necessary to cause a temperature change.
• Content: The heat energy necessary to cause a change in temperature is equal to the mass of the object time sits specific heat times the change in temperature.
• Level: 1

BACK to Ladder Heat Transfer and Temperature: Mathematical

$$Q = m c \Delta T$$

Symbol
Quantity
SI Unit
$$Q$$
Heat Energy Transferred
Joules (J)
$$m$$
mass
kilograms (kg)
$$c$$
Specific Heat of Substance
$$\frac{ \text{J} }{ \text{kg} \cdot ^{\circ} \text{C} }$$
$$\Delta T$$
Change in Temperature
Kelvin (K) or Degrees Celsius ($$^{\circ} \text{C}$$)

When using this formula, one of the key pieces is called the specific heat ($$c$$), also known as the heat capacity. This quantity depends on the material that is being heated up. You need to look it up in a reference table, then use it as a quantity in your equation.

Material
Specific heat $$\left( \frac{ \text{J} }{ \text{kg} \cdot ^{\circ} \text{C} } \right)$$
water
4184
oil
1900
wood
1800
aluminum
900
concrete
880
glass
800
steel
470
silver
235
gold
129
1. I have 2 kg of water. I heat it form 20°C to 30°C.
How much heat energy does the water absorb?
2. How much heat energy does it take to heat 0.5 kg of aluminum can from 20°C to 200°C?
3. How much energy does it take to heat 0.5 kg of water from its melting point (0°C) to its boiling point (100°C)?
4. You are at a major facility for melting large and molding large quantities of steel. How much energy does it take to heat 2000 kg of steel from 20°C to 800°C?

Usually, you will need to subtract in order to determine the change in temperature, but not always. Sometimes, change in temperature is given to you straight away.

1. How much energy does it take to heat of 3 kg of glass up by 4°C?
2. How much heat energy does it take to heat a 0.05 kg silver ring up by 40 degrees so it can be molded?

The heat energy added $$Q$$ can come out as a negative number! This happens when heat is removed from a substance. This will happen when the temperature goes down, or the final temperature is less than the initial temperature, and $$\Delta T$$ is negative.

1. What is the change in heat energy if you cool 3 kg of water from 50°C down to 37°C?
2. What is the change in heat energy if you cool 40 kg of oil from 30°C to 15°C?
3. What is the change in heat energy if you cool 2 kg of steel from 1500°C, where it solidifies, to a safe temperature of 20°C?
Extra Practice:

(Beyond here, you do not need to complete these problems in order to receive full credit for the practice page.)

1. A 0.5-kilogram piece of aluminum increases its temperature by 7°C when heat energy is added. How much heat energy was added?
2. A volume of water has a mass of 0.5 kilograms. If the temperature of this amount of water is reduced by 16°C, what is the change in heat energy?
3. How much energy is required to raise the temperature of 1 kilogram of steel by 10°C?
4. How much heat energy is needed to raise the temperature of 100-liters of water from 10°C to 25°C? (Note: One liter of water has a mass of one kilogram.)
5. What is the change in heat energy if you cool a 0.020 kg gold necklace from 300° to 20°?