Thermodynamics Test - 1

A single fixed point chosen as the basis of temperature scale is the Kelvin scale. The state in which ice, liquid water, and water vapor coexist in equilibrium, a state known as the triple point of water, provides the standard reference temperature. The temperature of the triple point of water, which can be very accurately and reproducibly measured, was assigned the value of 273.16 K, corresponding to 0.01°C, in order to maintain the magnitude of a unit temperature.

The power required by the fan will be equal to the rate of change of kinetic energy of the air which is caused by the fan.

The rate of change of kinetic energy of the air

dE = 1/2 × m˙×V²

where ṁ is the mass flow rate and V is the velocity of the air.

ṁ = ρ × Q

Calculation:

Given,ρ = 1.2 kg/m3, Q = 5 m3/s, V = 10 m/s

Assuming no heat loss in the fan, the power supplied to the fan 

dE = 1/2 × m˙× V²

dE = 1/2 × 1.2 × 5 × 10² = 300 W

Work done in a reversible isothermal process is given by 

W = C ln P₁/P₂ = C ln V₂/V₁

Where C = P₁V₁ = P₂V₂

P is the pressure and V is the volume of the gas. 

Calculation:

Given, P₁ = 1 bar, V₁ =  5 m³ and P₂ = 5 bar 

C = P₁V₁ = 1 bar × 5 m³ = 100 kPa × 5 m³ = 500 kJ

W = 500 ln(1/5) = −804.718 kJ

-ve sign shows that work is done on the system.

From the conservation of energy, Energy of the mixture = Sum of the energy of the individual streams.

The energy carried by flowing steam = mass flow rate × enthalpy/unit mass

Calculation:

Given, ṁ1 = 36 kg/min, ṁ2 = 14 kg/min, h₁ = 36 kJ/(kg da), h₂ = 50 kJ/(kg da)

Energy of the stream 1 = ṁ₁ × h₁ = 36 × 36 = 1296 kJ/(min da)

Energy of the stream 2 = ṁ₂ × h₂ = 14 × 50 = 700 kJ/(min da)

After the two streams mix into the one the resulting mass flow rate ṁ_mix = 36 + 14 = 50 kg/min

Now the energy of the resulting mass = h_mix × ṁf

From energy conservation E_mix = E₁ + E₂

⇒ h_f × 50 = 1296 + 700

⇒ h_mix = 1996/50 = 39.92 kJ/kg da

There are eight properties of a system, namely pressure (p), Volume (V), temperature (T), internal energy (u), enthalpy (h), entropy (s), Helmholtz function (f) and Gibbs function (g) and h, f and g are referred to as thermodynamic potentials.

Helmholtz function F = U - TS

Gibbs free function G = H - TS

The first law of thermodynamics gives the relationship between the heat transfer work transfer and the change in energy associated with a process. It is given by

dQ = ΔU + dW

where dQ is the heat interaction, dW is the work interaction and ΔU is the change in internal energy of the system.

Sign convention for the Heat and work transfer

If heat is added to the system it is treated as + ve and heat rejected by the system is treated as –ve.

If work is added to the system it is treated as –ve and work done by the system is treated as +ve.

Calculation:

Given, dW = -20 kJ/kg (work is done on the system)

dQ = -40 kJ/kg (Heat is added to the system)

Then, from first law of thermodynamics

ΔU = dQ – dW

ΔU = -40 + 20 = -20 kJ/kg