Question

Un gaz ideal efectuează o transformare la presiune constanta.Știind ca in cursul transformării temperatura creste cu 10% ,iar variația volumului este 0,5 l, volumul inițial ocupat de gaz are valoarea :
A. 5 L
B.2 dm cubi
C.4 dm cubi

Answer 1

[tex]\displaystyle Se~da:\\ \\ P_1=P_2=const.\\ \\ \frac {\Delta T}{T_1}=10\%=0,1\\ \\ \Delta V=0,5L=0,0005m^3\\ \\ V_1=?\\ \\ \\ Formule:\\ \\ \frac{\Delta T}{T_1}=0,1\Rightarrow \frac{T_1}{\Delta T}=10\\ \\ \\[/tex]


[tex]\displaystyle \Delta V=V_2-V_1\Rightarrow V_2=\Delta V+V_1\\ \\ \\ 1)P_1\times V_1=\nu\times R\times T_1\Rightarrow R=\frac{P_1\times V_1}{\nu\times T_1}\\ \\ \\ 2)P_2\times V_2=\nu\times R\times T_2\Rightarrow R=\frac{P_2\times V_2}{\nu\times T_2}\\ \\ R=\frac{P_2\times (\Delta V+V_1)}{\nu\times T_2}\\ \\ \\[/tex]


[tex]\displaystyle \frac{P_1\times V_1}{\nu\times T_1}=\frac{P_2\times (\Delta V+V_1)}{\nu\times T_2}\Leftrightarrow \frac{V_1}{T_1}=\frac{\Delta V+V_1}{T_2}\\ \\ V_1\times T_2=T_1\times\Delta V+T_1\times V_1\\ \\ V_1\times T_2-V_1\times T_1=\Delta V\times T_1\\ \\ V_1\times \Delta T=\Delta V\times T_1\\ \\ V_1=\frac{\Delta V\times T_1}{\Delta T}=10\times\Delta V\\ \\ \\ Calcule:\\ \\ V_1=10\times 0,0005=0,005=5L\\ \\ \\ Raspuns :a).[/tex]