I need help with this question Cylinder A contains oxygen (O 2 ) gas, and cylind

Question

I need help with this question

Cylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false?

(a)The two gases have different temperatures.

(b)The temperature of cylinder B is greater than the temperature of cylinder A    

(c)The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.

(d)The temperature of cylinder B is less than the temperature of cylinder A

Thank you so much. I will rate it if it correct

Explanation / Answer

Statement b is false

Formula of root mean square velocity v = ( 3RT/M)^1/2

According to question v1=v2

Here I use 1 for nitrogen and 2 For oxygen M for nitrogen is 14 and oxygen 16

From the formula

v1=v2

(3RT1/M1)^1/2= (3RT2/M2)^1/2

Squaring both side

T1/M1=T2/M2

To keep the ratio same as the M are different , T 1 and T2 must be different

So first statement is correct

From the relation

T1/M1= T2/M2

T1= M1/M2* T2 as M1 < M2 so T1 must be less than T2 to keep the ratio same

So second statement is false

Average kinetic energy depend on temperature so if T1 is less than T2 then K.E 1 will also be less than K.E2 hence third statement is true

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