First Law of Thermodynamics [Open and Closed Systems]

First law of thermodynamics

The first law of thermodynamics states that:

The algebraic sum of net heat and work interactions between a system and its surrounding in a thermodynamic cycle is zero

Mathematically

For a cyclic process

ΣQ = ΣW

Where:

Q = Heat interaction

W = Work interaction

For a finite non-cyclic process

Q_1-2 = W_1-2 + ΔE

Where:

E = Internal energy

In general

E = U + KE + PE + any other kind of stored energy

Where:

U = Intermolecular energy

KE = Kinetic energy

PE = Potential energy

For a closed system in equilibrium KE, PE and other kinds of stored energy are zero.

Which means

E = U

Hence for a finite non-cyclic process first law of thermodynamics becomes

Q_1-2 = W_1-2 + ΔU

If we consider only P*ΔV work, above equation becomes

Q_1-2 = P*ΔV + ΔU

Note: Conventionally work done by the system and the heat given to the system are always taken positive.

Internal energy

A property of a system whose change in a process executed by the system equal to the difference between the heat and work interactions by the system with its surrounding.

Enthalpy

Enthalpy is a thermodynamic quantity which is equal to total heat content in a system.

Mathematically

H = U + PV

According to the first law of the thermodynamics

Q_1-2 = P*ΔV + ΔU

Q_1-2 = P(V₂-V₁) + U₂ – U₁

Rearranging the above equation

Q_1-2 = U₂ + P₂V₂ – (U₁ + P₁V₁)

From the equation of enthalpy, it implies

Q_1-2 = H₂ – H₁

Specific heat

Specific heat is the quantity of heat which is required to raise the temperature of unit mass by one degree Celsius.

There are two types of specific heat

1. Specific heat at constant volume

C_v = ( ∂u/ ∂T)_v=constant

2. Specific heat at constant pressure

C_p = ( ∂h/ ∂T)_p=constant

First law applied to the open system (or control volume)

Unlike a closed system mass flows in and out of an open system. Here we have to take conservation of mass into account.

Conservation of mass

(dm1/dt) – (dm2/dt) = dm_cv/dt

Where

dm1/dt = Rate of mass entering to the system

dm2/dt = Rate of mass leaving from the system

dm_cv/dt = Rate of mass stored in the system

Conservation of energy

e = u + p*v + g*z + (V²/2)

Where

e = stored energy in the stream of fluid

u = internal energy stored in the stream of fluid

V²/2 = kinetic energy of the stream of fluid

g*z = potential energy stored in the stream of fluid

p*v = pressure work

Mathematical expression of first law for open system

(dm1/dt)*e1 + (∂Q/∂t) – (dm2/dt)*e2 – (∂W/∂t) = dE_cv/dt

At steady state

m1 = m2 = m

dE_cv/dt = 0

Hence the equation becomes

(dm/dt)*e1 + (∂Q/∂t) – (dm/dt)*e2 – (∂W/∂t) = 0

Above equation is also known as steady flow energy equation.

Also read:

What is a thermodynamic state?

Macroscopic approach to study thermodynamics

What is two property rule?

What is dead state of a system?

What is a point function?