2 kg of substance receives 500 kJ and undergoes a temperature change from 100°C to 200°C. The average specific heat of substance during the process will be
2.5 kJ/(kg°K)
Specific Heat: Understanding Thermal Properties
Specific heat is a fundamental property of a substance that tells us how much heat energy is required to raise the temperature of a unit mass of that substance by one degree Celsius (or one Kelvin). It's a crucial concept in thermodynamics and helps us understand how different materials store and transfer thermal energy.
Heat Transfer Calculation for the Substance
To determine the average specific heat of the substance during the process, we use the basic formula for heat transfer, which relates the heat absorbed, mass, specific heat, and temperature change.
Given Parameters:
- Mass of the substance (\(m\)) = 2 kg
- Heat received by the substance (\(Q\)) = 500 kJ
- Initial temperature (\(T_1\)) = 100°C
- Final temperature (\(T_2\)) = 200°C
Formula for Heat Received:
The amount of heat \(Q\) absorbed or released by a substance can be calculated using the formula:
\[ Q = m \cdot c \cdot \Delta T \]
Where:
- \(Q\) is the heat energy transferred (in Joules or kilojoules)
- \(m\) is the mass of the substance (in kg)
- \(c\) is the specific heat capacity of the substance (in J/(kgċK) or kJ/(kgċK))
- \(\Delta T\) is the change in temperature (\(T_2 - T_1\)) (in °C or K)
Temperature Change and Specific Heat Determination
First, let's calculate the temperature change (\(\Delta T\)) that the substance undergoes:
\[ \Delta T = T_2 - T_1 = 200^\circ C - 100^\circ C = 100^\circ C \]
It's important to remember that a change in temperature of 1°C is equivalent to a change in temperature of 1 Kelvin (K). Therefore, \(\Delta T = 100\) K.
Now, we can rearrange the formula \(Q = m \cdot c \cdot \Delta T\) to solve for the specific heat (\(c\)):
\[ c = \frac{Q}{m \cdot \Delta T} \]
Substitute the given values into the rearranged formula:
\[ c = \frac{500 \text{ kJ}}{2 \text{ kg} \cdot 100 \text{ K}} \]
\[ c = \frac{500}{200} \text{ kJ/(kg}\cdot\text{K)} \]
\[ c = 2.5 \text{ kJ/(kg}\cdot\text{K)} \]
The calculated average specific heat of the substance during the process is 2.5 kJ/(kg°K). This means that 2.5 kilojoules of energy are required to raise the temperature of 1 kilogram of this substance by 1 Kelvin (or 1 degree Celsius).
| Parameter | Value | Unit |
|---|---|---|
| Mass (\(m\)) | 2 | kg |
| Heat Received (\(Q\)) | 500 | kJ |
| Initial Temperature (\(T_1\)) | 100 | °C |
| Final Temperature (\(T_2\)) | 200 | °C |
| Temperature Change (\(\Delta T\)) | 100 | K (or °C) |
| Average Specific Heat (\(c\)) | 2.5 | kJ/(kg·K) |
This result aligns with one of the provided options, demonstrating a clear application of the specific heat formula to solve a practical thermal energy problem.
Important Questions from The Perfect Gas
The quantity of heat required to raise the temperature of unit mass of a material by one degree centigrade is called
The amount of heat required for converting one kilogram of a solid completely into liquid is called:
The heat that must be absorbed by ice of mass 500 g at – 10°C to take it to water at 20°C is (Specific heat of Ice is 2.2 kJ/kg K, Specific heat of water is 4.2 kJ/kg K and Latent heat of fusion of ice is 300 kJ/kg)
The general law for the expansion or compression of gases is:
Amount of energy required to raise the temperature of a substance of 1 kg mass by 1°C is called
