Calculate the root mean square speed of hydrogen molecules at 0 degree centigrade and 1 atm pressure. Assuming hydrogen to be an ideal gas. The density of hydrogen is 8.99×10^-2 kg/m3

Physics with Akhtiar Ali  Bullo

Physics class 12 numericals  12 class physics problems  Molecular Theory of Gases Numericals

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00:00Numerical number 8 of unit number 15 molecular theory of gases is. Calculate the root mean

00:16square speed of hydrogen molecules at 0 degree centigrade and 1 atm pressure. Assuming hydrogen

00:26to be an ideal guess, the density of hydrogen is 8.99 into 10 raised power minus 2 kilogram

00:36per meter cube. So first of all we will make a data,

00:43the temperature obtained is 0 degree centigrade, 0 degree centigrade is also equal to 273 Kelvin

01:11and pressure obtained is 1 atm. We can also write 1 atm as 1.01 into 10 raised power 5

01:30Pascal. Our density of hydrogen is given is means rho is given is 8.99 into 10 raised power

01:48minus 2 kilogram per meter cube is, mass of hydrogen molecule is equal to 2 into 1.67 into 10 raised power

02:14minus 27 kilogram. So, mass of hydrogen molecule will be equal to 3.34 into 10 raised power minus

02:3227 kilogram. And ball's main constant k is equal to 1.38 into 10 raised power minus 23

02:50joule per Kelvin. Hameh kya find karna hai? Hameh root mean square speed find karna hai. So,

02:57root mean square speed will be equal to watt. So, for calculation,

03:10we will use two methods, means we can make this calculation by two methods. So, first method

03:27root mean square speed is calculated by using formula under root 3 kt upon m. So, by putting the given values,

03:481.38 into 10 raised power minus 23 joule per Kelvin into temperature which is 273 Kelvin divided by mass of hydrogen

04:14which is 3.34 into 10 raised power minus 27 kilogram. So, root mean square speed will be equal to

04:321.38 into 10 raised power. So, we will use 1.38 into 10 raised power minus 23 divided by 3.34 into 10 raised power

05:00minus power minus 27. When we use, we have 1130.22 to divide 3.34 divided by 1.34 into 1130.22. So,

05:02When we have 1130.22 to 3.314 divide, then we have answer.

05:13Enter.

05:24So, root mean square speed will be equal to.

05:53Under root 338.389 into 10 raised power minus 23 plus 27.

06:16So, it will be 4.

06:19The under root of 338.389 is 18.395 into.

06:34The under root of 10 raised power 4 is 10 raised power 2 meter per second.

06:41Further, we will simplify this.

06:44Root mean square speed will be equal to.

06:4710 raised power 2 is also equal to 100.

06:50So, when we multiply 100 in values, this will become 18.39.5 meter per second.

07:02So, this is our answer by using first method.

07:09Now, second method.

07:24We can also calculate root mean square speed by using formula.

07:31So, root mean square speed is equal to under root 3p upon rho means density.

07:46The pressure is obtained is 1.01 into 10 raised power 5 Pascal divided by density.

08:01Density is also given which is 8.99 into 10 raised power minus 2.

08:08So, 3.03 divided by 8.99 into 10 raised power minus 2.

08:30So, 3.03 divided by 8.99, it will be under root 0.33704.

08:47So, root mean square speed will be equal to under root.

09:15equal to under root 0.33704 into 5 plus 2, it will be 7. So, also we can write this as

09:353.3704 into 10 is power 6. So, root mean square speeds will be equal to is the under root of

09:583.3704 is 1.8358 into the under root of 10 raised power 6 is 10 raised power 3

10:19meter per second. So, further हम इसको simplify करेंगे 10 cube जो है

10:30वो 1000 के equal होता है तो 1000 जब हम इस value के साथ multiply करेंगे

10:35तो हमें root mean square speed का जो final answer मिलेगा that will be

10:401835.8 meter per second. And we can also write it as

10:53जब हम इसको round off करेंगे तो हमें final answer मिलेगा

11:031836 meter per second. So, this is our answer by second method and this answer by first

11:17method. हमारे संदु टेक्स्ट के बुक में answer है वो यह है. So,

11:23इस method को हम preference देंगे to calculate root mean square speed in this numerical.

11:30उंगे तो में एक पुझा तो हमने का उन्साद करेंगे, तुझार,

11:37वह है कि जब हम इस दोने है को आप में आपक तो बुका के रिए

11:38तो हमारा सामेंस, रिए सब्बचल, भीन बपना चाहते है, जिए तो हमारा रावेशोय,

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