The First Law of Thermodynamics is based on the law of conservation of energy. It states that energy can neither be created nor destroyed but can only be transformed from one form to another. This law explains the relationship between heat, work, and internal energy in a thermodynamic system.
Statement of First Law of Thermodynamics
The mathematical expression of the first law of thermodynamics is given by:
Q = ΔU + W
Where:
- Q = Heat supplied to the system
- ΔU = Change in internal energy of the system
- W = Work done by the system
Pressure–Volume (P–V) Work
When a gas expands or contracts against an external pressure, work is done during the process. This mechanical work associated with a change in volume is called pressure–volume work (P–V work). The amount of work depends on the pressure acting on the gas and the change in its volume.
The work done is given by: W = P ΔV
Where:
- P = external pressure acting on the system
- ΔV = change in volume of the system
Sign Convention
- If the gas expands (ΔV > 0), work is done by the system therefore, W is positive.
- If the gas is compressed (ΔV < 0), work is done on the system therefore, W is negative.
Change in Internal Energy
Internal energy is the sum of the microscopic kinetic and potential energies of all the molecules present in a system. It includes the kinetic energy due to molecular motion and the potential energy due to intermolecular forces. The internal energy of a system changes whenever heat is exchanged or work is done.
- Heat supplied to the system increases its internal energy.
- Heat lost by the system decreases its internal energy.
- Work done by the system decreases its internal energy.
- Work done on the system increases its internal energy.
- Internal energy is a state function and depends only on the initial and final states of the system.
Energy Conservation
The First Law of Thermodynamics is based on the principle of conservation of energy. It states that energy cannot be created or destroyed but can only be converted from one form to another. In a thermodynamic process, energy is transferred between the system and its surroundings in the form of heat and work.
- Energy exchanged as heat or work changes the internal energy of the system.
- The total energy of the system and surroundings remains constant.
- The First Law of Thermodynamics is a direct consequence of the law of conservation of energy.
Limitations of First Law of Thermodynamics
Although the First Law of Thermodynamics explains the conservation of energy, it does not provide complete information about thermodynamic processes. It cannot predict the direction in which a process will occur or whether a process is possible under given conditions.
- It does not explain the natural direction of heat flow.
- It does not indicate whether a process is spontaneous or non-spontaneous.
- It does not explain the irreversibility of natural processes.
- It does not specify the maximum efficiency of heat engines.
Perpetual Motion Machine of First Kind (PMM-1)
A Perpetual Motion Machine of the First Kind is a hypothetical machine that continuously produces work without receiving any energy from an external source. Such a machine would violate the law of conservation of energy because it would create energy from nothing.
- PMM-1 contradicts the First Law of Thermodynamics.
- No machine can produce continuous work without energy input.
- Therefore, a perpetual motion machine of the first kind cannot exist in reality.
Solved Examples
Example 1: Find out the internal energy of a system that has a constant volume and the heat around the system is increased by 30 J.
Solution:
Given that,
Heat Transfer, ΔQ = 30 J
For constant volume, ΔV = 0
W = P ΔV = 0
The formula for internal energy is given as:
ΔU = ΔQ - W
⇒ ΔU = 30 J - 0
⇒ ΔU = 30 J
Hence, the change in internal energy of the system is 30 J.
Example 2: Calculate the change in the internal energy of the system if 2000 J of heat is added to a system and work of 1500 J is done.
Solution:
Given
Heat added to a system, ΔQ = 2000 J
Work done on the system, W = 1500 J
The formula for internal energy is given as:
ΔU = Q + W
⇒ ΔU = 2000 J + 1500 J
⇒ ΔU = 3500 J
Hence, the change in internal energy of the system is 3500 J.
Example 3: A gas in a closed container is heated with 20 J of energy, causing the lid of the container to rise 3 m with 4 N of force. What is the total change in energy of the system?
Solution:
Given
Heat supplied to the container, ΔQ = 20 J
Rise in lid of the container, Δx = 3 m
Force applied on the container, F = 4 N
We are not given a value for work, but we can solve for it using the force and distance. Work is the product of force and displacement.
W = F Δx
⇒ W = 4 N × 3 m
⇒ W = 12 J
The formula for internal energy is given as:
ΔU = ΔQ - W
⇒ ΔU = 20 J - 12 J
⇒ ΔU = 8 J
Hence, the change in internal energy of the system is 8 J.