digraph physicsDerivation { 
overlap = false;
label="derivation: coefficient of thermal expansion using the equation of state for an ideal gas
https://allofphysiscs.com";
fontsize=12;
0003744460 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0003744460 -> generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd;
generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd.png",labelloc=b];
0003037920 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0003037920 -> generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea;
generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea.png",labelloc=b];
0008295331 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd -> 0008295331;
generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3464107376_b204568feb0026bcae7a8406e85afcf7df313fccd4e7037bc1e520ad74239cfd.png",labelloc=b];
generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea -> 0008295331;
generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3497828859_02807a1da7a8b7556d2dfc8bcda92b1dcea5a0318573689d58b12317ce04b6ea.png",labelloc=b];
0008295331 -> generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399;
generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399.png",labelloc=b];
0005311790 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_simplify.png",labelloc=b];
generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399 -> 0005311790;
generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1311403394_078f5ba886046d5076845728bfc88947e6be7b2615c21d8cd99094726bffa399.png",labelloc=b];
0005311790 -> generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72;
generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72.png",labelloc=b];
0002439511 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0002439511 -> generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf;
generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf.png",labelloc=b];
0005713113 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dividebothsidesby.png",labelloc=b];
generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf -> 0005713113;
generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8435841627_891b1b16ffbdac831cbb1b29f23c3b922e345a21edd2e6c6f461cc1c6c339adf.png",labelloc=b];
0005713113 -> generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14;
generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14.png",labelloc=b];
generated_feed_7924842770_e632b7095b0bf32c260fa4c539e9fd7b852d0de454e9be26f24d0d6f91d069d3 -> 0005713113;
generated_feed_7924842770_e632b7095b0bf32c260fa4c539e9fd7b852d0de454e9be26f24d0d6f91d069d3 [shape=box, color=red,label="",image="/code/static/generated_feed_7924842770_e632b7095b0bf32c260fa4c539e9fd7b852d0de454e9be26f24d0d6f91d069d3.png",labelloc=b];
0003078632 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteRHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72 -> 0003078632;
generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5962145508_8868168247f36edf61578e7164bcf476883927d34226d72837d26b611ae24c72.png",labelloc=b];
generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14 -> 0003078632;
generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2613006036_2b79193579d75b4c1b0701f27b728b2b1692477b5bfb5d860d90191e1e55fb14.png",labelloc=b];
0003078632 -> generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d;
generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d.png",labelloc=b];
0001997333 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_simplify.png",labelloc=b];
generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d -> 0001997333;
generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6925244346_20b92eb0c97c74aeb2b0d5dabb89fbfc5eae65350d6875c7b2ad7182752e358d.png",labelloc=b];
0001997333 -> generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939;
generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939.png",labelloc=b];
0006216231 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declarefinalexpression.png",labelloc=b];
generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939 -> 0006216231;
generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2472653783_db8a5d1a4a0bf7251093cb69cb4005c6d9faa60bae7355e2fa43da7248601939.png",labelloc=b];
}