Properties of Gases MCQ Quiz in मल्याळम - Objective Question with Answer for Properties of Gases - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

For two coupled cycle in series

\(\begin{array}{l} \eta = 1 - \left( {1 - {\eta _1}} \right)\left( {1 - {\eta _2}} \right)\\ = 1 - \left[ {1 - {\eta _1} - {\eta _2} + {\eta _1} \cdot {\eta _2}} \right]\\ = {\eta _1} + {\eta _2} - {\eta _1} \cdot {\eta _2} \end{array}\)

Explanation:

Dalton’s law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

Suppose there are n1 moles of gas A1, n2 moles of gas A2, n3 moles of gas A3,… and up to nk moles of gas Ak, are there in a homogeneous mixture of inert ideal gases at a temperature T, a pressure P, and a volume V.

Since there is no chemical reaction, the mixture is in a state of equilibrium with the equation of state

pV = (n1 + n2 + n3 + …+ nk) R̅ .T Where, R̅ is universal gas constant.

and R̅ = 8.3143 kJ / kg-mol-K

\(p = \frac{{{n_1}\bar R\ T}}{V} + \;\frac{{{n_2}\bar R\;T}}{V} + \frac{{{n_3}\bar R\;T}}{V} + \ldots + \frac{{{n_k}\bar R\;T}}{V}\)

As \({p_1} = \;\frac{{{n_1}\bar R\;T}}{V},\;{p_2} = \frac{{{n_2}\bar R\;T}}{V},\;{p_3} = \frac{{{n_3}\bar R\;T}}{V}, \ldots {p_k} = \frac{{{n_k}\bar R\;T}}{V}\)

Thus, p = p1 + p2 + p3 +…+ pk

Explanation:

Polytropic Process is represented by:

PVn = C

where P is pressure, V is volume, and n is the polytropic index.

• The isothermal process is governed by Boyle’s law.
• The temperature remains constant in this process. Pressure and volume are inversely proportional to each other. Hence, when P increases V decreases, and when V increases P decreases.
• Thus the curve developed is a rectangular hyperbola. So, the graph for the Isothermal process shows a hyperbolic curve.

T = C

i.e. PV = C (from ideal gas equation)
where P = Pressure, T = Temperature, V = Volume

Concept:

• The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.

\({C_v} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;volume}}\)

• The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

\({C_p} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;pressure}}\)

• The relation between the ratio of Cp and Cv with a degree of freedom is given by

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

Where f = degree of freedom

EXPLANATION:

• The relation between the ratio of Cp and Cv with a degree of freedom is given by

\(\Rightarrow \gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

Monoatomic gas has 3 degrees of freedom

\(\Rightarrow \gamma = 1 + \frac{2}{3} = \frac{3 +2}{3} = \frac{5}{3} =1.67\)

Explanation:

The steam may be in any one of the following three conditions:

• Saturated steam which may be either wet or dry
• Superheated steam
• Supersaturated steam

​​​Saturated steam:

• Steam which is formed in contact with water is known as saturated steam.
• If heat is supplied to the saturated vapour and to the liquid with which it is in contact, more liquid evaporates but the temperature remains the same. Similarly, if heat is removed, more of the vapour condenses but the temperature will remain the same.
  • If saturated steam contains liquid particles, then it is known as wet steam.
  • If saturated steam does not contain any liquid particles, then it is known as dry saturated steam.

Superheated Steam:

If the temperature of the steam is greater than the boiling point temperature corresponding to the pressure of steam generation, then it is called superheated steam.

Concept:

The initial condition is P₁, V₁

And the final condition is \({P_2} = \frac{{{P_1}}}{2}\), V₂ = 3V₁

Hyperbolic/Isothermal Process:

T = C i.e. PV = C 

Here: \(P_2V_2=\frac{P_1}{2}(3V_1)\ne P_1V_1\)

Polytropic Process:

PVⁿ = C

\({P_1}V_1^n = {P_2}V_2^n\)

\( \Rightarrow {P_1}V_1^n = \left( {\frac{{{P_1}}}{2}} \right){\left( {3{V_1}} \right)^n }\)

\( \Rightarrow V_1^n = \frac{{{3^n }}}{2}V_1^n \)

⇒ 3ⁿ = 2

⇒ For n < 1 ⇒ n = 0.63

Adiabatic Process:

In adiabatic process, γ = 1.4

Concept:

• The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.

\({C_v} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;volume}}\)

• The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

\({C_p} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;pressure}}\)

• The relation between the ratio of Cp and Cv with a degree of freedom is given by

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

Where f = degree of freedom

For mono atomic gas f = 3

For Diatomic gas f = 5

Calculation:

Given:

Gas is diatomic i.e. f = 5

We know that,

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{5}\)

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = \frac{7}{5}\)

Concept:

A perfect gas is also an Ideal gas, which follows the Ideal gas equation of states i.e. PV = mRT all temperature.

where, P = pressure of gas, V = volume occupied, m = mass of a gas, R = universal gas constant. 

The universal gas constant (R) is the difference between specific heat constants for constant pressure (C_p) and constant volume (C_v)

i.e.R = C_p - C_v

A real gas behaves as an Ideal gas at low pressure and very high temperature. Air is a perfect gas.

Gases that obey the gas laws (Charles law, Boyles law, and Universal Gas Law) are called ideal gases.

Boyle’s, Charles’, and Gay Lussac's Laws describe the basic behavior of fluids with respect to volume, pressure, and temperature.

The Combined gas law or General Gas Equation is obtained by combining Boyle's Law, Charles's law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature for a fixed mass (quantity) of gas:

\(\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\)

\({C_P} - {C_V} = \frac{R}{J}\) is valid for a perfect gas only.

CONCEPT:

Adiabatic index:

• The adiabatic index is also known as the heat capacity ratio and is defined as the ratio of heat capacity at constant pressure CP to heat capacity at constant volume CV.

​It is given as,

\(\Rightarrow γ=\frac{C_P}{C_V}\)

EXPLANATION:

• From the above table, it is clear that the adiabatic index for the monoatomic gas is equal to 5/3. Hence, option 3 is correct.

Key Points

• The correct method for determining the speed of sound in gas is using a "Household Tube" technique, also known as the Kundt's tube experiment.
• This method involves using acoustic standing waves within a tube to measure the wavelength of the sound in the gas.
• By knowing the frequency of the sound and measuring the wavelength in the gas, the speed of sound can be calculated using the formula (\(v = f \lambda\)) , where (v) is the speed of sound, (f) is the frequency, and (\(\lambda\)) is the wavelength.
• The Kundt's tube experiment is a practical and visual method, allowing direct measurement of the wavelength of sound in a controlled environment.

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