dW =<latexit sha1_base64="p2pKbrtowhn2vs33AUlQeuvGVL4=">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</latexit>

なんでP dV

でマイナス（ー）がつきますか？

ここが躓きの最初の一歩！？

大気圧の代わりにおもりを置く
重力は鉛直下方におもりの位置エネルギーは増加した+mgh<latexit sha1_base64="KNxko9s7XrE2qf6f33fBPI9Nrcc=">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</latexit>

エネルギー保存則からおもりの位置エネルギーが増加した場合，その分何かのエネルギーが減少して差し引きゼロとなる

h<latexit sha1_base64="/4O7GHZ8aTPU9hv3x1Pzf7Gloos=">AAACZHichVFNSwJBGH7cvswsLQmCICQxOskYUtFJ6tLRj/wAE9ndxlxcd5fdVTDpD9S16NCpICL6GV36Ax38A0F0NOjSodd1IUqqd5iZZ555n3eemZEMVbFsxroeYWR0bHzCO+mb8k/PBIKzc3lLb5oyz8m6qptFSbS4qmg8Zyu2youGycWGpPKCVN/p7xda3LQUXduz2wYvN8RDTakqsmgTla5VghEWY06Eh0HcBRG4kdKDt9jHAXTIaKIBDg02YRUiLGolxMFgEFdGhziTkOLscxzDR9omZXHKEImt03hIq5LLarTu17QctUynqNRNUoYRZU/sjvXYI7tnL+zj11odp0bfS5tmaaDlRiVwspB9/1fVoNlG7Uv1p2cbVWw6XhXybjhM/xbyQN86uuhltzLRzgq7Zq/k/4p12QPdQGu9yTdpnrmEjz4g/vO5h0F+LRZfjyXSiUhy2/0KLxaxjFV67w0ksYsUcnQuxynOcO55FvxCSJgfpAoeVxPCtxCWPgHZOonx</latexit>

気体

人がエネルギーを与えた
その分マイナス

気体がエネルギーを与えた

気体のエネルギーは減少した

おもりの位置エネルギーは増加した

位置エネギーの変化 ＝Z h<latexit sha1_base64="1tkGIJEb/i7QvoCRK1jst0brRFs=">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</latexit>

外力0z

Fext dz =Z h(+mg)dz = +mgh (*)

0h<latexit sha1_base64="/4O7GHZ8aTPU9hv3x1Pzf7Gloos=">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</latexit>(*)おもりが気体からされた仕事は正の量である。

気体

逆に気体（人）の立場からみれば気体がおもり（外界）に仕事をしたのでその分の気体のエネルギー変化は負の量となる。

大気圧

微小変化

dh > 0<latexit sha1_base64="RzN5R4m2AU7ySf2Q4DMblDMv6cE=">AAACb3ichVG7SgNBFD1Z3/EVtVAQZDEo2oQbCSoWItpYqjEqGAm7m0myuC92N4EY/AE/QAsLHyAifoaNP2CRTxArUbCx8GazICrqHWbmzJl77pyZUR1D93yiekRqaW1r7+jsinb39Pb1xwYGtzy77Goio9mG7e6oiicM3RIZX/cNseO4QjFVQ2yr+yuN/e2KcD3dtjb9qiP2TKVo6QVdU3ymsrWsa8r5w5K8KFMuFqcEBSH/BMkQxBHGmh27RhZ52NBQhgkBCz5jAwo8brtIguAwt4cacy4jPdgXOESUtWXOEpyhMLvPY5FXuyFr8bpR0wvUGp9icHdZKWOCHuiGXuiebumR3n+tVQtqNLxUeVabWuHk+o9G0m//qkyefZQ+VX969lHAfOBVZ+9OwDRuoTX1lYOTl/TCxkRtki7pif1fUJ3u+AZW5VW7Whcbp4jyByS/P/dPsDWTSM4mUuup+NJy+BWdGMU4pvi957CEVawhw+c6OMYZziPP0rA0JsnNVCkSaobwJaTpD1ffjcQ=</latexit>

気体の圧力P<latexit sha1_base64="UzSmZiKYc6Tcn8FuL4Twj+PjuQo=">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</latexit>

気体がピストンを押す力<latexit sha1_base64="jlDvyL7uOze0ADMj/vqSW2ci2A8=">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</latexit>

P = F/AdW =気体

仕事

ピストンの面積F dh =
力 距離☞このマイナスが大事！気体が仕事をしてエネルギーがその分減ったことを意味する

P Adh =

P dV
体積の変化
＝ピストンの面積 移動距離

気体の体積V ! V + dV<latexit sha1_base64="oTQBzTwMji1yy1g68UNbu2AawxI=">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</latexit>

気体の体積：膨張の時は3<latexit sha1_base64="WEQlTkx5jzS1fYF3GAhgVFVsyU4=">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</latexit>

1.0 m ! 1.0 + 0.0001 m

気体3dV > 0<latexit sha1_base64="8c58XyeuCjjx67JWG6HjalLyGKM=">AAACcHichVFNLwNBGH66vuujxaWJg6Uh4tC8lQZxEOHiiGpJaGR3TWvT/bK7bULjD/gDDi4qERE/w8UfcOhPEDckLg7ebjcRBO9kZp555n3eeWZGdQzd84kaEamtvaOzq7sn2tvXPxCLDw7lPbviaiKn2YbtbquKJwzdEjlf9w2x7bhCMVVDbKnlleb+VlW4nm5bm/6RIwqmUrL0oq4pPlOF2q5ryvsneXlRJnkvnqQUBSH/BOkQJBHGmh2/xi72YUNDBSYELPiMDSjwuO0gDYLDXAE15lxGerAvcIIoayucJThDYbbMY4lXOyFr8bpZ0wvUGp9icHdZKWOCHuiGXuiebumR3n+tVQtqNL0c8ay2tMLZi50msm//qkyefRx8qv707KOI+cCrzt6dgGneQmvpq8dnL9mFjYnaJF3SE/uvU4Pu+AZW9VW7Whcb54jyB6S/P/dPkJ9JpWdTmfVMcmk5/IpujGAcU/zec1jCKtaQ43MPcYYL1CPPUkIalcZaqVIk1AzjS0jTH5zIjdw=</latexit>dW =<latexit sha1_base64="G3wsQGhjB1NjMCN8i5FIIviZLrg=">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</latexit>

P dV < 0気体の体積

V ! V + dV<latexit sha1_base64="oTQBzTwMji1yy1g68UNbu2AawxI=">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</latexit>

気体の体積：圧縮の時は気体

3<latexit sha1_base64="nvXIRKLuZwIixB83w61sMiaZABk=">AAACmnichVHLThRBFD00IjiADLAx0UWFCcaNk9vyMqwIbCRueA2QMDDpbouhQr9SXTMGJ/yAP8CClSaEEL/CuDG6dsEnEJaYuGHB7Z6OBAl4O1116txzbt2qcmNfJYbotMPqfND1sLvnUaG3r//xQHFwaDWJGtqTFS/yI73uOon0VSgrRhlfrsdaOoHryzV3dy7NrzWlTlQUrpi9WG4GTj1U28pzDFO14oRdJlEVolXVgQj2t8ZEVav6jnG0jt6LNPlSUJmIbFb9FdWKpYzkELeBnYMS8liIiseo4h0ieGgggEQIw9iHg4S/DdggxMxtosWcZqSyvMQ+CuxtsEqywmF2l8c6rzZyNuR1WjPJ3B7v4vOv2SkwSr/ohC7oO32hM7q8s1Yrq5H2ssez2/bKuDbw8cnyn/+6Ap4Ndq5d9/ZssI3XWa+Ke48zJj2F1/Y3PxxcLE8vjbae02c65/4/0Sl94xOEzd/e0aJcOkSBH8D+97pvg9VXZXuyPL44XpqZzZ+iB08xghd831OYwRssoML7HuIrfuCn9cyateatt22p1ZF7hnEjrJUrt5OaTA==</latexit>

1.0 m ! 1.0

0.0001 m

気体が外界から仕事をされてエネルギーが増加

3dV < 0<latexit sha1_base64="RhlJWFHCupOJDK0HPvV0CoQtcms=">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</latexit>dW =<latexit sha1_base64="IFTBsYAepLGLi0vqjMUMPrBd3ZI=">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</latexit>

P dV > 0