Sure! Below is a sample work related to thermal energy, detailing calculations and explanations for different scenarios.
Sample Problem 1: Calculating Heat Transfer
Problem Statement:
A metal block with a mass of 2 kg is heated from an initial temperature of 25°C to 75°C. If the specific heat capacity of the metal is 0.9 J/g°C, how much heat energy is required?
Given Data:
- Mass (m): 2 kg = 2000 g (since 1 kg = 1000 g)
- Initial Temperature (T_initial): 25°C
- Final Temperature (T_final): 75°C
- Specific Heat Capacity (c): 0.9 J/g°C
Formula:
The heat transfer (\( Q \)) can be calculated using the formula:
\[
Q = m \cdot c \cdot \Delta T
\]
where \( \Delta T = T_{final} - T_{initial} \).
Calculation Steps:
-
Calculate the change in temperature (\( \Delta T \)):
\[ \Delta T = T_{final} - T_{initial} = 75°C - 25°C = 50°C \] -
Substitute values into the heat transfer formula:
\[ Q = 2000 , g \cdot 0.9 , \frac{J}{g°C} \cdot 50°C \] \[ Q = 2000 \cdot 0.9 \cdot 50 \] \[ Q = 90000 , J \]
Answer:
The heat energy required is 90,000 Joules.
Sample Problem 2: Phase Change
Problem Statement:
How much heat is needed to melt 1 kg of ice at 0°C to water at 0°C? The specific latent heat of fusion of ice is 334,000 J/kg.
Given Data:
- Mass (m): 1 kg
- Specific Latent Heat of Fusion (L): 334,000 J/kg
Formula:
The heat required for a phase change can be calculated using the formula:
\[
Q = m \cdot L
\]
Calculation Steps:
- Substitute the values into the formula:
\[ Q = 1 , kg \cdot 334,000 , \frac{J}{kg} \] \[ Q = 334,000 , J \]
Answer:
The heat required to melt the ice is 334,000 Joules.
Sample Problem 3: Heating a Substance
Problem Statement:
You have 0.5 kg of water that needs to be heated from 20°C to 100°C. The specific heat capacity of water is 4.18 J/g°C. How much heat energy will this require?
Given Data:
- Mass (m): 0.5 kg = 500 g
- Initial Temperature (T_initial): 20°C
- Final Temperature (T_final): 100°C
- Specific Heat Capacity (c): 4.18 J/g°C
Formula:
\[
Q = m \cdot c \cdot \Delta T
\]
Calculation Steps:
-
Calculate the change in temperature (\( \Delta T \)):
\[ \Delta T = T_{final} - T_{initial} = 100°C - 20°C = 80°C \] -
Substitute values into the heat transfer formula:
\[ Q = 500 , g \cdot 4.18 , \frac{J}{g°C} \cdot 80°C \] \[ Q = 500 \cdot 4.18 \cdot 80 \] \[ Q = 167200 , J \]
Answer:
The heat energy required to heat the water is 167,200 Joules.
Summary
These sample problems illustrate different aspects of thermal energy calculations including heating and phase changes. The formulas for calculating heat transfer, latent heat, and specific heat capacity are essential for understanding thermal energy in different contexts. If you have any specific scenario or additional questions, feel free to ask!