Solved Examples on First Law of Thermodynamics

Example 1: Find out the internal energy of a system that has 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 a work of 1500 J is done.

Solution:

Given that,

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 = ΔQ – W

⇒ ΔU = 2000 J – 1500 J

⇒ ΔU = 500 J

Hence, the change in internal energy of the system is 500 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 that,

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.

Example 4: Determine the change in the internal energy of the system when gas in a cylinder is fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 2 liters to a volume of 5 liters. So it absorbs 100 J of thermal energy from its surroundings. 

Answer:

Given that,

Q = 100 J

V₁ = 2 L 

V₂ = 5 L 

Then, according to the formula:

ΔU = Q – PΔV

⇒ ΔU = Q – P(V₂ – V₁)

Therefore,

ΔU = Q – P(V₂ – V₁)

⇒ ΔU = 100 J – 1 (5 – 2) 101.33 J

⇒ ΔU = -203.99 J

First Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body’s Internal Energy.

The First Law of Thermodynamics states that energy cannot be created or destroyed however, it can be transferred from one form to another. Also, according to the first law of thermodynamics, Heat is a form of energy and the thermodynamic processes (like Isothermal, Isochoric, Adiabatic, Isothermal, and Quasi-Static Processes.) obey the Law of Conservation of Energy.