consider an ideal gas confined in an isolated closed

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $${V^q},$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: $$\left( {\gamma = \frac{{{C_p}}}{{{C_v}}}} \right)$$

A. $$\frac{{\gamma + 1}}{2}$$

B. $$\frac{{\gamma - 1}}{2}$$

C. $$\frac{{3\gamma + 5}}{6}$$

D. $$\frac{{3\gamma - 5}}{6}$$

Answer : $$\frac{{\gamma + 1}}{2}$$

Solution :
$$\eqalign{ & \tau = \frac{1}{{\sqrt 2 \pi {d^2}\left( {\frac{N}{V}} \right)\sqrt {\frac{{3RT}}{M}} }} \cr & t\mu \frac{V}{{\sqrt T }} \cr & {\text{As, }}T{V^{\gamma - 1}} = K \cr & {\text{So, }}\tau \, \propto \,{V^{\gamma + \frac{1}{2}}} \cr & {\text{Therefore, }}q = \frac{{g + 1}}{2} \cr} $$

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Heat and Thermodynamics >> Thermodynamics

Releted Question 1

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

A. $$PV$$

B. $$2PV$$

C. $$\frac{1}{2}PV$$

D. zero

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Releted Question 2

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A. 1.40

B. 1.50

C. 1.53

D. 3.07

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Releted Question 3

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A. same everywhere

B. lower in the front side

C. lower in the rear side

D. lower in the upper side

View Answer

Releted Question 4

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

A. $$4\, RT$$

B. $$15\, RT$$

C. $$9\, RT$$

D. $$11\, RT$$

View Answer

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $${V^q},$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: $$\left( {\gamma = \frac{{{C_p}}}{{{C_v}}}} \right)$$

Releted MCQ Question on
Heat and Thermodynamics >> Thermodynamics

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

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Thermodynamics

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Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $${V^q},$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: $$\left( {\gamma = \frac{{{C_p}}}{{{C_v}}}} \right)$$

Releted MCQ Question on Heat and Thermodynamics >> Thermodynamics

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

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Thermodynamics