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Q.

Two gases of molecular masses M_A and M_B are at temperatures T_A and T_B respectively. T_AM_B = T_BM_A, which one of the following properties has the same value for both gases ?

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a

Pressure

b

Kinetic energy

c

RMS velocity

d

Density

answer is C.

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Detailed Solution

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$when \frac{T_{A}}{M_{A}} = \frac{T_{B}}{M_{B}} T_{A} M_{B} = T_{B} M_{A} {(PV)}_{A} = nRT {(PV)}_{A} = \frac{W_{A}}{M_{A}} {RT}_{A} {(PV)}_{B} = \frac{W_{B}}{M_{B}} {RT}_{B} ∴ when W_{A} = W_{B} {(PV)}_{A} = {(PV)}_{B} V_{rms} = \sqrt{\frac{3 RT}{M}} V_{A} = \sqrt{\frac{3 {RT}_{A}}{M_{A}}} V_{B} = \sqrt{\frac{3 {RT}_{B}}{M_{B}}} V_{A} = V_{B} (∵ \frac{T_{A}}{M_{A}} = \frac{T_{B}}{M_{B}})$

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