One mole of an ideal diatomic gas is taken through the cycle as shown in the figure- 1 - 2 - Isochoric process 2 - 3 - Straight line on P-V diagram 3 - 1 - Isobaric process The average molecular speed of the gas in the states 1-2 and 3 are in the ratioA- 1- 2- 2 B- 1- -2- -2C- 1- 1- 1D- 1- 2- 4

The correct option is A 1: 2: 2Applying the ideal gas equation, At (1) P_oV_o = (1) RT_1 ⇒ T_1= P_0V_0R = x (say) At (2) nbsp; (4P_0) (V_0) = (1)RT_2 ⇒ T_2 = ...

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Standard XII

Physics

Gas laws from KTG

One mole of a...

Question

One mole of an ideal diatomic gas is taken through the cycle as shown in the figure.
$1 \to 2$ : Isochoric process
$2 \to 3$ : Straight line on P-V diagram
$3 \to 1$ : Isobaric process
The average molecular speed of the gas in the states $1, 2$ and $3$ are in the ratio

1 : 2 : 2

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1 : \sqrt{2} : \sqrt{2}

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1 : 1 : 1

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1 : 2 : 4

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Solution

The correct option is A $1 : 2 : 2$
Applying the ideal gas equation,
At $(1)$
$P_{o} V_{o} = (1) R T_{1} \Rightarrow T_{1} = \frac{P_{0} V_{0}}{R} = x (s a y)$
At $(2)$
$(4 P_{0}) (V_{0}) = (1) R T_{2} \Rightarrow T_{2} = \frac{4 P_{0} V_{0}}{R} = 4 x$
At $(3)$
$P_{0} (4 V_{0}) = (1) R T_{3} \Rightarrow T_{3} = \frac{4 P_{0} V_{0}}{R} = 4 x$
We have for the molecules of the gas, $V_{a v} = \sqrt{\frac{8 R T}{π M}} \Rightarrow V_{a v} \propto \sqrt{T}$

$V_{1} \propto \sqrt{x} V_{2} \propto \sqrt{4 x} V_{3} \propto \sqrt{4 x}$

$∴ V_{1} : V_{2} : V_{3} = 1 : 2 : 2$

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One mole of an ideal diatomic gas is taken through the cycle as shown in the figure. 1→2 : Isochoric process 2→3 : Straight line on P-V diagram 3→1 : Isobaric process The average molecular speed of the gas in the states 1,2 and 3 are in the ratio

The correct option is A 1:2:2Applying the ideal gas equation, At (1) PoVo=(1)RT1⇒T1=P0V0R=x(say) At (2) (4P0)(V0)=(1)RT2⇒T2=4P0V0R=4x At (3) P0(4V0)=(1)RT3⇒T3=4P0V0R=4x We have for the molecules of the gas, Vav=√8RTπM⇒Vav∝√T V1∝√xV2∝√4xV3∝√4x ∴V1:V2:V3=1:2:2

One mole of an ideal diatomic gas is taken through the cycle as shown in the figure.
$1 \to 2$ : Isochoric process
$2 \to 3$ : Straight line on P-V diagram
$3 \to 1$ : Isobaric process
The average molecular speed of the gas in the states $1, 2$ and $3$ are in the ratio