[理工] [化熱]活塞彈簧組

看板Grad-ProbAsk作者 ( )時間12年前 (2011/12/24 21:03), 編輯推噓2(207)
留言9則, 2人參與, 最新討論串1/2 (看更多)
Consider the cylinder filled with air and with the piston and spring arrangement shown below. The external atmosphere pressure is 1 bar, the initial temperature of the air is 25度C, the no-load length of the spring is 50 cm, the spring constant is 40000 N/m, the frictionless piston weighs 500kg, and the constant-volume heat capacity of air can be taken to be constant at 20.3J/mol‧K . Assume the air is ideal gas.Compute how much heat must be added to the gas in the cylinder for the spring to compress 2 cm? ──────── § ↑ 1 bar § 55 cm │ § │ │↓ § ↓│ ┌────┐←piston └────┘ │ │↑ │ │15 cm │ │ └────┘↓ Ans:Q=1026.5J W=-207.5J 想請問這題該如何算 我在算出初始的壓力、莫耳數後,利用第一定律算出了內能變化量 但卻苦於不知道如何算W 謝謝大家 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 203.67.161.40 ※ 編輯: kohtak 來自: 203.67.161.40 (12/24 21:12)

01/07 00:50, , 1F
W(活塞和大氣壓)
01/07 00:50, 1F

01/07 00:50, , 2F
=-∫ Pex dv=-(Patm+mg/A)*ΔV=-(Patm+mg/A)*A*ΔX
01/07 00:50, 2F

01/07 00:50, , 3F
W(彈簧)=
01/07 00:50, 3F

01/07 00:50, , 4F
-∫Fdx=-∫K(X-X0)dx=-(1/2)*[(X2-X0)^2-(X1-X0)^2]
01/07 00:50, 4F

01/07 00:51, , 5F
X2=0.53 X1=0.55 X0=0.50 ΔX=0.02
01/07 00:51, 5F

01/07 01:02, , 6F
或者直接W=-∫FdX F=Patm*A+mg-k(x-x0)
01/07 01:02, 6F

01/07 01:03, , 7F
這裡的A都是指活塞的底面積
01/07 01:03, 7F

01/07 01:03, , 8F
說錯 應該說是圓柱體的底面積
01/07 01:03, 8F

01/17 12:23, , 9F
感激不盡!!!!!
01/17 12:23, 9F
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文章代碼(AID): #1EzSshnA (Grad-ProbAsk)