Question

Am o problema la fizica,si am nevoie de V2 scos din formula asta P1V1 la puterea gama =P2V2 la puterea gama.P1=3,2*10^5 Pa,P2=10^4 Pa si V1=2 dm^3

Answer 1

[tex]\displaystyle p_1\times V_1^\gamma=p_2\times V_2^\gamma\\ \\ \text{Avem gaz monoatomic, deci } \gamma=\frac 53\\ \\ p_1\times V_1^\frac 53=p_2\times V_2^\frac 53\\ \\ \text{Din matematica stim ca }x^\frac ab=\sqrt[b]{x^a},\text {de aceea:}\\ \\ p_1\times \sqrt[3]{V_1^5}=p_2\times\sqrt[3]{V_2^5}\\ \\ \text{Ridicam la cub amindoua parti:}\\ \\ (p_1\times \sqrt[3]{V_1^5})^3=(p_2\times\sqrt[3]{V_2^5})^3\\ \\ p_1^3\times V_1^5=p_2^3\times V_2^5\\ \\ \text{Exprimam }V_2^5:\\ \\ [/tex]

[tex]\displaystyle V_2^5=\frac{p_1^3\times V_1^5}{p_2^3}\\ \\ \text{Luam radacina de ordin 5 din ambele parti:}\\ \\ \sqrt[5]{V_2^5}=\sqrt[5]{\frac{p_1^3\times V_1^5}{p_2^3}}\\ \\ \text{Obtinem:}\\ \\ V_2=V_1\times\sqrt[5]{\frac{p_1^3}{p_2^3}}\\ \\ \text{Calculam:}\\ \\ V_2=0,002\text{(In SI)}\times \sqrt[5]{\frac{(3,2\times 10^5)^3}{(10^4)^3}}=0,016m^3[/tex]