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In this quesn, how they have assumed thta final pressure of both the vessels will be same.
![question image](https://images.topperlearning.com/topper/new-ate/topr_18933240212331377doubt.jpeg)
Asked by aaryamanmodern | 17 Jan, 2023, 22:18: PM
Initially both vessels of equal volume V is at same pressure Po and absolute temperature To .
Let n be number of moles in each vessel . Hence we write ideal gas equation as
![begin mathsize 14px style P subscript o space left parenthesis 2 V right parenthesis space equals space left parenthesis 2 n right parenthesis space R space T subscript o end style](https://images.topperlearning.com/topper/tinymce/cache/fb9d70d05de94f804e7ad7ac75af11e0.png)
where R is universal gas constant. Hence we write
![begin mathsize 14px style left parenthesis 2 n right parenthesis space equals space fraction numerator P subscript o space left parenthesis 2 V right parenthesis over denominator R space T subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/497c29b569dce4352e2a2e1d0a24b9d5.png)
If one vessel is maintained at temperature To and other one is maintained at temperature T1 ( T1 > To ) ,
then vessel at temperature To will have more number of moles and vessel at temperature T1
will have less number of moles because both vessels are connected by a narrow tube
and they are at equal pressure.
Let n1 be the number of moles in the vessel that is maintained at temperature To .
Let n2 be the number of moles in the vessel that is maintained at temperature T1 .
Then we have ,
.............................(2)
![begin mathsize 14px style n subscript 1 space equals space fraction numerator P space V over denominator R space T subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/a5e6fc835b3adf9c4a0a241ece1212c8.png)
and
......................................(3)
![begin mathsize 14px style n subscript 2 space equals space fraction numerator P space V over denominator R space T subscript 1 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/20b67fc8d3ac1460b436481ccd166dbf.png)
By adding eqn.(2) and (3) , we get
![begin mathsize 14px style n subscript 1 space plus space n subscript 2 space equals space fraction numerator P space V over denominator R space end fraction open parentheses 1 over T subscript o space plus space 1 over T subscript 1 close parentheses space end style](https://images.topperlearning.com/topper/tinymce/cache/89941fd2879bc19f5e60154c3c851375.png)
Since number of moles in both vessels remain constant, n1 + n2 = ( 2 n )
Hence we equate eqn.(1) and (4) to get
![begin mathsize 14px style space fraction numerator P space V over denominator R end fraction open parentheses 1 over T subscript o plus 1 over T subscript 1 close parentheses space space equals space space fraction numerator P subscript o space left parenthesis 2 V right parenthesis over denominator R space T subscript o end fraction space space end style](https://images.topperlearning.com/topper/tinymce/cache/7b6ab6c94bd63bd6cd7939690d61dc9a.png)
![begin mathsize 14px style P space open parentheses fraction numerator T subscript o plus T subscript 1 over denominator T subscript o space T subscript 1 end fraction close parentheses space equals space fraction numerator 2 space P subscript o over denominator T subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/a5237dd49c440dc478b55c2145d4c4a2.png)
![begin mathsize 14px style P space equals space fraction numerator 2 space P subscript o over denominator T subscript o end fraction space cross times space fraction numerator T subscript o space T subscript 1 over denominator T subscript o plus T subscript 1 end fraction space equals space P subscript o space cross times fraction numerator 2 space T subscript 1 over denominator T subscript o plus T subscript 1 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/f2f0938ab66647530cee7d702baf0598.png)
Let us substitute values , Po = 105 kPa , To = 300 K and T1 = 400 K
P = 105 × ( 800/700) = 120 kPa
Answered by Thiyagarajan K | 17 Jan, 2023, 23:40: PM
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