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Behaviour of Perfect Gas and Kinetic Theory

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Q 1. In an adiabatic process, the root mean square speed of the molecules of a monoatomic gas becomes twice its initial value. The ratio of the initial volume of the gas to the final volume is

{tex}2{/tex}

{tex} 2 ^ { 3 / 2 } {/tex}

{tex}4{/tex}

{tex}8{/tex}

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Q 2. A gas in a closed container has temperature {tex} T {/tex} and pressure {tex} P . {/tex} If the molecules of the gas undergo inelastic collisions with the walls of the container, then

both {tex} P {/tex} and {tex} T {/tex} will decrease

{tex} P {/tex} decreases and {tex} T {/tex} increases

{tex} P {/tex} increases and {tex} T {/tex} decreases

both {tex} P {/tex} and {tex} T {/tex} remain the same

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Q 3. A vessel contains {tex} 4 {/tex} moles of oxygen and {tex} 2 {/tex} moles of argon at absolute temperature {tex} T {/tex}. The total internal energy of the gas mixture is

{tex} 6 R T {/tex}

{tex} 9 R T {/tex}

{tex} 11 R T {/tex}

{tex} 13 R T {/tex}

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Q 4. The mass of an oxygen molecule is about {tex}16{/tex} times that of a hydrogen molecule. At room temperature the rms speed of oxygen molecules is {tex} v {/tex}. The rms speed of the hydrogen molecule at the same temperature will be

{tex} v / 16 {/tex}

{tex} v / 4 {/tex}

{tex} 4 v {/tex}

{tex} 16 v {/tex}

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Q 5. Two thermally insulated vessels 1 and 2 are filled with air at temperature {tex} \left( T _ { 1 } , T _ { 2 } \right) , {/tex} volume {tex} \left( V _ { 1 } , V _ { 2 } \right) {/tex} and pressure {tex} \left( P _ { 1 } , P _ { 2 } \right) {/tex} respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

{tex} T _ { 1 } + T _ { 2 } {/tex}

{tex} \left( T _ { 1 } + T _ { 2 } \right) / 2 {/tex}

{tex} T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) / \left( P _ { 1 } V _ { 1 } T _ { 2 } + P _ { 2 } V _ { 2 } T _ { 1 } \right) {/tex}

{tex} T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) / \left( P _ { 1 } V _ { 1 } T _ { 1 } + P _ { 2 } V _ { 2 } T _ { 2 } \right) {/tex}

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Q 6. {tex} 0.014 \mathrm { kg } {/tex} of nitrogen is enclosed in a vessel at a temperature of {tex} 27 ^ { \circ } \mathrm { C } {/tex}. The amount of heat energy to be supplied to the gas to double the rms speed of its molecules is approximately equal to

{tex} 6350 \mathrm { J } {/tex}

{tex} 7350 \mathrm { J } {/tex}

{tex} 8350 \mathrm { J } {/tex}

{tex} 9350 \mathrm { J } {/tex}

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