Calculating the Amount of Heat Transferred

Oct 13, 2025 by wbrum.org 92 views

Understanding the Problem

When dealing with heat transfer, it's essential to understand the concept of specific heat capacity, which is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). In this problem, we are given 50 g of liquid water with a specific heat capacity of 4180 J/kg·K. We need to calculate the amount of heat transferred when the temperature of the water changes from 298 K to 348 K in a calorimeter.

Calculating the Amount of Heat Transferred

To calculate the amount of heat transferred, we can use the formula:

Q = mcΔT

where:

Q is the amount of heat transferred (in Joules, J)
m is the mass of the substance (in kilograms, kg)
c is the specific heat capacity of the substance (in J/kg·K)
ΔT is the change in temperature (in Kelvin, K)

First, we need to convert the mass of the water from grams to kilograms:

50 g = 0.05 kg

Next, we need to calculate the change in temperature:

ΔT = T2 - T1 = 348 K - 298 K = 50 K

Now, we can plug in the values into the formula:

Q = mcΔT = (0.05 kg) × (4180 J/kg·K) × (50 K) = 10490 J

To convert the amount of heat transferred from Joules to kiloJoules, we can divide by 1000:

Q = 10490 J / 1000 = 10.49 kJ

Rounding to one decimal place, we get:

Q ≈ 10.5 kJ

Conclusion

In this problem, we calculated the amount of heat transferred when 50 g of liquid water changes temperature from 298 K to 348 K in a calorimeter. We used the formula Q = mcΔT and plugged in the values to get the answer. The correct answer is A. 10.5 kJ.

Discussion

This problem is a great example of how to calculate the amount of heat transferred in a calorimeter. It's essential to understand the concept of specific heat capacity and how to use the formula Q = mcΔT to solve problems like this. If you have any questions or need further clarification, feel free to ask.

Key Concepts

Specific heat capacity: the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin)
Heat transfer: the transfer of heat energy from one substance to another
Calorimeter: a device used to measure the amount of heat transferred in a reaction

Practice Problems

A 100 g sample of copper has a specific heat capacity of 385 J/kg·K. If the temperature of the copper changes from 20°C to 50°C, how much heat is transferred?
A 200 g sample of water has a specific heat capacity of 4180 J/kg·K. If the temperature of the water changes from 10°C to 30°C, how much heat is transferred?

Solutions

Q = mcΔT = (0.1 kg) × (385 J/kg·K) × (30 K) = 1155 J
Q = mcΔT = (0.2 kg) × (4180 J/kg·K) × (20 K) = 16760 J

Understanding Heat Transfer

Heat transfer is the transfer of heat energy from one substance to another. It's an essential concept in chemistry, physics, and engineering. In this article, we'll answer some frequently asked questions about heat transfer in a calorimeter.

Q: What is a calorimeter?

A: A calorimeter is a device used to measure the amount of heat transferred in a reaction. It's typically a sealed container that surrounds the reaction mixture, allowing the heat to be transferred to a surrounding medium, such as water or air.

Q: What is specific heat capacity?

A: Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It's a measure of a substance's ability to absorb or release heat energy.

Q: How do I calculate the amount of heat transferred?

A: To calculate the amount of heat transferred, you can use the formula:

Q = mcΔT

where:

Q is the amount of heat transferred (in Joules, J)
m is the mass of the substance (in kilograms, kg)
c is the specific heat capacity of the substance (in J/kg·K)
ΔT is the change in temperature (in Kelvin, K)

Q: What is the difference between heat transfer and heat capacity?

A: Heat transfer is the transfer of heat energy from one substance to another, while heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin).

Q: Can you give an example of heat transfer in a calorimeter?

A: Yes, let's say we have 50 g of liquid water with a specific heat capacity of 4180 J/kg·K. If the temperature of the water changes from 298 K to 348 K, we can calculate the amount of heat transferred using the formula:

Q = mcΔT = (0.05 kg) × (4180 J/kg·K) × (50 K) = 10490 J

Q: What are some common applications of heat transfer in a calorimeter?

A: Some common applications of heat transfer in a calorimeter include:

Measuring the heat of reaction in a chemical reaction
Determining the specific heat capacity of a substance
Measuring the heat transfer rate in a heat exchanger
Studying the thermal properties of materials

Q: Can you give some tips for working with heat transfer in a calorimeter?

A: Yes, here are some tips:

Make sure to use a well-insulated calorimeter to minimize heat loss
Use a thermometer to measure the temperature of the substance accurately
Use a precise balance to measure the mass of the substance accurately
Use a data logger to record the temperature and heat transfer data accurately

Q: What are some common mistakes to avoid when working with heat transfer in a calorimeter?

A: Some common mistakes to avoid include:

Not using a well-insulated calorimeter, leading to heat loss
Not using a precise balance, leading to inaccurate mass measurements
Not using a thermometer, leading to inaccurate temperature measurements
Not recording the data accurately, leading to errors in calculations

Conclusion

Heat transfer in a calorimeter is an essential concept in chemistry, physics, and engineering. By understanding the principles of heat transfer and using the correct formulas and techniques, you can accurately measure the amount of heat transferred in a reaction. Remember to use a well-insulated calorimeter, precise balances and thermometers, and record the data accurately to avoid common mistakes.