Thermodynamics

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During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio $\frac{C_{P}}{C_{V}}$ for the gas is

$\frac{4}{3}$

2

$\frac{5}{3}$

$\frac{3}{2}$

Solution

$\frac{3}{2}$

Given, that

$ρ \propto T^{3}$

⇒ $ρ T^{- 3} = constant$ .....(i)

Also for adiabatic process,

$ρ V^{γ} = Constant$

But pV = RT (ideal gas law)

⇒ V = $\frac{RT}{ρ}$

∴ $ρ {(\frac{RT}{ρ})}^{γ} = constant$

$ρ^{1 - γ} T^{γ}$ = constant ..... (ii)

⇒ $ρ T^{\frac{γ}{(1 - γ)}}$ = constant

Equating Eqs. (i) and (ii), we get

$\frac{γ}{1 - γ} = - 3$

⇒ $γ = - 3 + 3 γ$

⇒ 2γ = 3

⇒ $γ = \frac{3}{2}$

⇒ $\frac{C_{P}}{C_{V}} = \frac{3}{2}$

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Thermodynamics

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio $\frac{C_{P}}{C_{V}}$ for the gas is

$\frac{4}{3}$

2

$\frac{5}{3}$

$\frac{3}{2}$

Some More Questions From Thermodynamics Chapter

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is

(R = 8.3 J mol⁻¹ K⁻¹ )

Which of the following is incorrect regarding the first law of thermodynamics?

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Which of the following statements is correct for any thermodynamic system?

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal

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Column-1	Column-2
P. Process I	a. Adiabatic
Q. Process II	b. Isobaric
R. Process III	c. Isochoric
S. Process IV	d. Isothermal

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Thermodynamics

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio CPCV for the gas is 43 2 53 32

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When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is(R = 8.3 J mol−1 K−1 )

Which of the following is incorrect regarding the first law of thermodynamics?

A system goes from A to B via two processes I and II as shown in the figure. If ∆U1 and ∆U2 are the changes in internal energies in the processes I and II respectively, the

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Thermodynamic processes are indicated in the following diagram.Match the following Column-1 Column-2 P. Process I a. Adiabatic Q. Process II b. Isobaric R. Process III c. Isochoric S. Process IV d. Isothermal

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio $\frac{C_{P}}{C_{V}}$ for the gas is

$\frac{4}{3}$

2

$\frac{5}{3}$

$\frac{3}{2}$

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is

(R = 8.3 J mol⁻¹ K⁻¹ )

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal