Delta E = q + w, Problems based on Delta e equals q plus w?

The equation ∆E or Delta E = q + w represents the First Law of Thermodynamics, i.e., the law of conservation of energy. It is important to understand energy transformations taking place within a system.

As per the First law of Thermodynamics:

‘Energy cannot be created or destroyed. It can be converted from one form to another. Therefore, the total energy of a system stays conserved. The energy lost to the surroundings is equal to the energy gained by the thermodynamic system and vice versa’’.

U = q + w …equation (i)

Where,

• U = internal energy (the total energy content of a system)
• q = heat (energy exchanged between the system and its surroundings)
• w = work-done (force applied x distance moved in the direction of applied force)

What is Delta E = q + w?

Equation (i) can alternately be written as:

∆ E = q + w …equation (ii)

Where the Greek symbol delta (∆) denotes change, thus, 

• ∆E (Delta E) = change in energy (Unit: Joules, J)
• q = heat exchanged (Unit: Joules, J)
• w = work-done (Unit: Joules, J)

If the change in energy is positive (∆E > 0), that means a certain amount of heat (q) is absorbed by the system, which leads to work done on the system (+w).

Contrarily, if the change in energy is negative (∆E < 0), it implies that the thermodynamic system releases a particular amount of heat (q), which means work done by the system (-w).

Where and how to use Delta E = q + w? – Examples

The formula ∆ E = q + w can be used to find the change in energy if the values of heat (q) and work done (w) are given.

Moreover, ∆ E = q + w can be rearranged to make q or w the subject of the formula, depending upon which variable is unknown.

Now let’s see through the examples given below how to apply Delta E = q + w for solving numerical problems.

For example, If the amount of heat transferred from the surroundings to the system is 400 J and the work done by the system is 300 J, find the change in the internal energy of the system.

Solution

As per the question statement;

Heat absorbed from the surrounding to the system = q = + 400 J

Work done by the system = w = – 300 J

Change in internal energy = ∆E =?

Applying the formula,

Substituting the known values to find Delta E:

∆ E = 400 + (-300)

∆ E = 400 – 300

∴ ∆ E = 100 J

Result: The change in internal energy of the system is 100 J.

Another example is- What is the change in internal energy of the system if the heat transferred from the system to the surroundings is 400 J and the work done on the system is 300 J?

Solution

 As per the question statement;

The heat released from the system to the surrounding = q = – 400 J

Work done on the system = w = +300 J

Change in internal energy = ∆E =?

Applying the formula,

⇒ ∆ E = q + w

Substituting the known values to find Delta E:

∆ E = -400 + (-300)

∆ E = -400 -300

∴ ∆ E = -700 J

Result: The change in internal energy of the system is – 700 J.

More Examples on ∆E (Delta E) = q + w

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