Một lượng khí được nén đẳng nhiệt từ thể tích 10,0 lít đến 4,0 lít, áp suất khí tăng thêm 0,75 atm. Áp suất ban đầu của khí là
Một lượng khí được nén đẳng nhiệt từ thể tích 10,0 lít đến 4,0 lít, áp suất khí tăng thêm 0,75 atm. Áp suất ban đầu của khí là
A. \(0,3\;{\rm{atm}}.\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- $V_1 = 10 \; l$
- $V_2 = 4 \; l$
- $P_2 = P_1 + 0.75$
$P_1 * 10 = (P_1 + 0.75) * 4$
$10P_1 = 4P_1 + 3$
$6P_1 = 3$
$P_1 = 0.5 \; atm$
Vậy áp suất ban đầu của khí là 0,5 atm. Tuy nhiên, không có đáp án nào trùng khớp hoàn toàn. Xem xét lại đề bài, áp suất khí *tăng thêm* 0.75 atm. Vậy ta có:
$P_1V_1 = P_2V_2$
$P_1 * 10 = (P_1 + 0.75) * 4$
$10P_1 = 4P_1 + 3$
$6P_1 = 3$
$P_1 = 0.5 atm$.
Nếu áp suất ban đầu là $P_1$, thì áp suất sau là $P_2 = P_1 + 0.75$. Theo định luật Boyle: $P_1V_1 = P_2V_2$ hay $P_1(10) = (P_1 + 0.75)(4)$. Giải ra ta được $10P_1 = 4P_1 + 3$, suy ra $6P_1 = 3$ hay $P_1 = 0.5$. Vậy có lẽ các đáp án có vấn đề.
Nếu áp suất tăng *gấp* 0.75 lần thì $P_2 = 0.75 P_1$ và $P_1*10=0.75P_1*4$ => $10=3$ (vô lý).
Nếu áp suất sau bằng 0.75 atm, thì $P_1 = P_2 - 0.75$. Vậy $P_1 = -0.75 + 0.75=0 atm$ (vô lý).
Kiểm tra lại phép tính, có lẽ mình đã hiểu sai ý.
$P_1 * V_1 = P_2 * V_2$
$P_1 * 10 = (P_1 + 0.75) * 4$
$10P_1 = 4P_1 + 3$
$6P_1 = 3$
$P_1 = 0.5 atm$.
Có lẽ đề bài hoặc đáp án bị sai. Giả sử áp suất tăng lên *3 lần* chứ không phải 0.75 atm:
$P_1 * 10 = (P_1 + 3) * 4$
$10P_1 = 4P_1 + 12$
$6P_1 = 12$
$P_1 = 2 atm$.
Có lẽ đáp án gần đúng nhất là 0.5 atm, nhưng không có trong lựa chọn.
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