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### 1102-H: Heat Formula 3

• Topic Cluster: Thermodynamics
• Topic: Heat Transfer and Temperature: Mathematical
• Objective: Solve heat formula problems asking for final or initial temperature.
• Content: Given the amount of heat added to an object, its mass, and its specific heat, a physicist can determine the intital or final temperature of the object.
• Level: 3

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The goal of this pod is to solve problems in which you are looking for final temperature or initial temperature of an object. These are a little bit more algebraically difficult than solving for other variables. To these problems, it can be helpful to use a different version of the formula.

$$Q = m c \Delta T \; \; \; \; \; \; \; \; \; \; Q = m c \left( T_f - T_i \right)$$

Symbol
Quantity
SI Unit
$$Q$$
Heat Energy Transferred
Joules (J)
$$m$$
mass
kilograms (kg)
$$c$$
Specific Heat of Substance
$$\frac{ \text{J} }{ \text{kg} \cdot ^{\circ} \text{C} }$$
$$T_f$$
Final Temperature
Kelvin (K) or Degrees Celsius ($$^{\circ} \text{C}$$)
$$T_i$$
Initial Temperature
Kelvin (K) or Degrees Celsius ($$^{\circ} \text{C}$$)
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 0.800 kg of water with a temperature of 30.0°C. I add 10,000. Joules of energy to the water. What will be the final temperature?
2. A gold ring has a temperature of 22°C and a mass of 200 grams. If a metal worker adds 5624 Joules of heat energy to the ring, what is its final temperature?
3. A massive concrete building has a temperature of 5°C and a mass of 4000 kilograms at night. The sun rises and adds $$6.69 \cdot 10^7$$ Joules of heat energy to the building. What is its final temperature?
4. Somebody heats a bowl of 3 kg of water to its boiling point (100°C) by adding 941400 Joules of heat energy. What was its initial temperature?
5. By rubbing wooden sticks together, somebody adds 7560 Joules of heat energy. The sticks have a mass of 0.200 kg, and they reach a final temperature of 35°C. What was their initial temperature?
6. Someone has been cooking with a hot pot, but after taking it off the heat it returns to room temperature. The pot is mostly steel and has a mass of 0.85 kg. It gives off 47141 Joules of heat energy when it reduces its temperature of 22°C. What was its initial temperature?

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