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Answer to Question #5546 in Molecular Physics | Thermodynamics for cncrowell

Question #5546
One mole of the ideal gas is initially at 4 atm
and 2 L. As the gas is slowly heated, the
plot of its state on a PV diagram moves in a
straight line to the state 5 atm and 7 L.
Find the work done by the gas.
Answer in units of kJ
Expert's answer
The work done by the gas
data:image/png;base64,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
Density as a function of volume - is linear:
data:image/png;base64,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
Let’s find the necessary constants.
data:image/png;base64,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
So we have
data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA3cAAACTCAIAAACibHdIAAAUSElEQVR4nO3dWaLiIBBG4V6XC3I9WY2bcTH2g17NQEEVFEPC+d66b8wAKL8Q4r8XAAAA4O1f7xMAAADABZEyAQAA4I+UCQAAAH+kTAAAAPgjZQIAAMAfKRMAAAD+SJkAAADwR8oEAACAP1ImAAAA/JEyAQAA4I+UCQAAAH+kTAA4etz/fd2W5+d/n8st9N8AgABSJgCEfBLlPkt+/vv+6HRaAHAapEwACHrnyX2cfNzJmACgQsoEgKBQynwuNzImAOiQMgEg7HHfzZiTMQHAgJQJAGH7lPm4s+QHAPRImUksNQUmtZ0yJ2MCgA0pU4GlppjI+mvV7F+h1imTjAkAVqRMDZaawtdmKHygPPdOmN8T+TvNC7byXZb+J1zn903+XG77Ctrt4oKFBACFSJkaLDWFr7/4NkCw3DiM171PdLTT9PaXF4WUeVsex3f7pqjC30MBYHakTBWWmsLVqCnzYPaU+Rt0jr/bn8vt+sUEAFakTBWWmsJVxZR5mAo+DsEZpukP368uKZ0yE98o+dYJACGkTBWWmsJV3bHMX5IM7j/x5/1pTtDU5ZSpufuaiAkAAlLm22aE59itstQUrirPmP81Z2H3nz+ngtE8y9siKTOFiAkAMlJmcorxtw1LTeGkcsqM7/7dYBPtdJ6I+cpPmXzjBICo6VPm9lmYYv/LUlN4qr365xObQrvXrOeZbYAuK2XuC+lxn6nIAEBj9pS5j5XS4ARLTeGpX8pML+eZLWK+slJm6ImnvPEBYGvulKn/9R6WmsJTr5SZHmwP3xJy8fxUcF8mAEA2dcq0/EQkS03hqHbKDP8oqi5jhly8WZMyAaCKmVOm8PPkBTujk4JOo5S5bZHpyfLgzy5OEL9ImQBQxcwpU/k8F+WeLj6nCFfVf/vn2Li5ZVhGygSAKiZOmV5DmSw1hVnzlMnTD2JImQBQxbwpU7meR7sblprCoHXKnOrpl3akTACoYt6USceCfqqnzM1I/Rw/Rl6ADwMAqGL6lEnfiw5apkxuyEwiZQJAFdOmzOrdPCBrmDKZLE8jZQJAFdOmTPoVdFT/S867gd9uLPpR4NMAAKqYNWV+F+3Qr6CDVimT4XoVUiYAVEHKpF9Be/VTJreEGJAyAaCKWVPmX7dCH4wemqVMcpMGKRMAqiBldkiZrMeYvggYaRwKKRMAqpg0ZX4nzBv38k6Pgh/Y+pew44Vb+igp/ZEGRMpUaFfDpExnz+VGYcKKZjOskqqJpczDz9ocP+mFX2lcdw9Dfnp3uS3zs+q3rLtMFO3+z/3GalWFWzqtuzvSGQrnjZSplG5LHpV+nZR5KI1EG7NuvxH64TOpHjJO/fy1cRonbjbVaefddpelvo6ceb1j+UeK31BZ6qo57DNW/amxzN/OQsUQmXcee4nr9+yaNWmXiLnelbi7/iW//w3tqKKgeXzx8IXzRspUUrWl4kq/QMr89Q+ri/xeuThAoN4+fsyArKbd/oN5ctdoNrWo5zzfG3630s5Z2udUf2UX6vR2x7NXlqlq1NWenDGPfP4Gr2H/wjE/LVp/mDlmzFc03K/+XJLbys7UeLUFOTNwpJqF42eKlNmuLZVW+nVS5r4ExFkb6/byMT0LbYr3xUiu0Wwq2OYtzc1f221SnzmW/R9fJlTL7g/2yrJVjfZjU5syo6OVob969DDVNL4t03u5b/yj+F0vuQdzqDd7kMs9aKhgaxaOnyl603ZtqbTSL5MypX7j+Cfr9pZj5hvvfTF0R1buGs3G1/7XeRP1L3TvcnIy7j/wWrn8NzuyV1ZWykyefDJlCnH478eRF2Go4XEf+a3ZNmX6DmT+9hgZ8s4/WPmHak6mzszhwZKtWDh+xutNK2jYlgor/QIpU2S9NsP2M6RM/0/vczhVs3k97roPCU09bjZLBykpIYkvNe5fx/bGEStrrJT5uWM1OiQ77kd205RZ4WMqMcBc3q+X7CHrerNiZvhIFQvHz3i9aQUN21JhpV84ZVpbmmX7CVKmVwo4m1M1G83bN/Mtnqx/+RZM1c2Z3ilTdXlyZfVNmYGFm6sB39Bo0sjvS+Pdyh7HMi2F+fc7vc+YsS5IObx9i5PB9nrj9+6KL4uc2td9sc1UDPXVR/+hrGwSI2rYlgor/cIp09qNWbY/ecqMP34gshDi/tj9/e+Vwl1k6wOdpImdq9mk3sH57+/kdUU20JSJU8q0XWBqMn+IlPlcbtt3mupmAN0ZG+TXTMPFP+J4urDh6pTkLBzeqcub12fG/d/9EfiYVtzcImzSqXDqtUlVb2q56hE1bEuFld4yZbb8oLMNcZi3P2nKDExlicvHEp/fq372WK+HMFpSnTSbFOlNXPTmTgWpWIM1DLEWtXfjmyZWWZ1SZmCQ6W8g8xV6D2a3oIumTN1QZmRMOPTiYDvxGUEuTAa/C3ncf+eXWAK83kZ+loH29kvHwumZMo1NYkQN21JhpV80ZdYNC98P+3t0TDDrjFukzO0xhM+TRMr8+yK0LLffNr/FFZv/Lut2aDYKx/dx6Tt78JQpr+NJvSL8AlvV1EuZm/m6w3tw+Mny12v99bJ6r6IaypQ2Sq7vX52+1zRqYTL43Eh3v29/KEDxOSQVQqJwAnusVzh+Ur2pvUkMqGVbKqv0U4V3LfU0Sub235esS63wC3zDlBlcPC39d+J9KrRG1Xeh0Zyx2ays38oOb+tRU2b8bg9RsrJMVVMtZX6W/YRPeqhb32SDpUwpL0VeG4z+WWtnLAw3EYYnNDNSZqfCqS3Rm2Zc9Zu1Sq2Ew/ZvS2WVfsGUabofPGP75J6ydlWWMotSXLgAdClTGAFV3zM+jnM2m/CePPY3asoMnEJ6L7mVlbgXwTtl7scHtm+ybQIdl9R/1TtU1lRxpE1Eo79ShWQgvuUUxRCdIZYKJ7hDj8KpLd6b5jSJN2uVWgmH7d+Wyir9aimzwXhUem85uytKmb9WWDAl7ZIypTeqbzm7O22zOdDco2XZ0cgpc30akWOVVJZwlX4pc3UL/vGze/3H8aYlJe1TZqTyU4kieI6bFuN6l0LRLKd4yoovUbGbpWxxq17h+Il+omY1iQG1bEtllX6tlBn5BuayvXKHOcVZljTMxw18O5o3ZZ642YT349HJO6RMzURmeSkmcnVhZYWrpkbKDMTIVcosHTJqeHezcNdMFal8lbgdUTjF1aucw31JMhA/Q3PvG+hdOH1W/+Rd9YBatqWySr/Q6p/1F/8a22v0Spnmw6wPNPhYJs3GvhOH1pQMUvJJq+7f8Bs4iJReeWU1S5mhGPn9Y3nWuWjKTH2uhP+eunP09yrv+eCCZJAKBtGzDL44fq9m/cIZKWU2vJnYS8u2VFbpl0mZ3cejVnt1T5nP5eZxqkLvH02Z0qVcJGWevdnIeyidOk8HqZIJvAopUzoPlyHd6inzfo/cI3U7y2T56/VKppQqB5MOFfoUey63v9/ulF72aTk393UtBclAanOqVh4sptEKx48iZVqvejxN21JRpV9kxlwsHSGfWbcPvFrbgJWS74vyXsYYDOM96SVmzM/fbFanJdag7wdRehPdAKI1ZZpLz1JZ1p37pczoPdW/AZYzfUA3TZmpkLV/bzzeaX7bRp/LLfgtwv8TKz8ZRFtiaofCW3KwwvGjuS/TeNXjadqWiir9EilTLu5wPrNsH1pdIH1/Lhmeibwviu7yPR5CmioQguHvD89l9WQt18jaxxWaTerV+UFT88kQPLZyBDG2f0vpRW8k0lautWoqpMxYxh3rfZPQeu5RGTO/fmupfouubsvjGZhL9i/37M/y0K1O6q/u4ve+sQrHT/wUs656PE3bUlGlXyFlpqZUxftONNtHOrzwf2aWpNjZlA50RXf1XG7v57LGjhwqGCmbCpchRtmOrtBsNGknK2iuLjb6ukOTeuimneL7j5beenvxzWGsXGvV+KdM8U4Za8111zwap8bOwyPCsTHkKjdfr3acORx0Ww4/tKY6w1gOH6lw/KQyUcZVj6dpWyqq9POnzEMWOgjfjKLcXspHod2UzngariLX7rRvy3Pzf5FkFXw3bv60L5K/nQmb93WBZvN6vV6vx13xMfO46w6SuMj4LbqKy9HuXyi94MujY6GWS7FUjWPKvJwOA7B17pauwWteynzIMT51W+k53BrozeucRoe2lOn8KRMAmiJlytrelrk56Bl63MZmzJidUmZoIjo8BTMbUiYAWKhnskmZrY87c2d+MGfEfPVNmcJiyBmr4Q8pEwAM9J33zCmzQ95zvIf99EZcb9lMx5QZeVLEtM2SlAkAWqYVOROmzP7r4h/36Tu02YtgrGXw04es6QsAAHSsT66dOWXSpaCXoVLmUCfTBSkTAKqYOGXO26eiu6Ea4dT3LrxeL1ImAFQyYcrseFsm8DZQyuReYVImAFQyccqkR0E3w6RMMubrxWcCAFQyX8ocpn/HxAZphaf87a4KSJkAUMW8KZMOBf0MkTI/2Yp3AikTAOqYL2Wy1AH99U+ZDGOukDIBoIrpUiZDmRhA75TJ71BtkDIBoIrpUmZoKPP7k5ObP/x+9Zn+GM66psxpf9dTRMoEgCpmS5nxn3IW/pu+B846pkyGMY9ImQBQxWwpU1rwEP6J59l/BxG1dEuZYsZ8Lrd5oycpEwCqmCxlioOToZT5XG70O6iiU8p8HzZ0UOtP014LKRMAqpgrZcqd7LufWf+FjIl6+qTM9Q3IIaRM3u8A4OnqKfNxX/Wd774k3JPsU+bmhYCvHilzs5wtaNqQFUyZLAoEgFIXT5nrwcvIQOZrP2VOxkRVvZ9khA1hLJNFgQBQZoqUqRl7WKdMMiYqI2UORZoxZ1EgABSZKGUmOvRv1yEvtiV9wgkpcyiWlMkN2wCgdvGUafC5MfMR7EN+t2gRC+CAlDkUcfUPiwIBoAQp889v2DPQ1TCTDlekzKGoUyYfAQBgQcr8o/iBc7oYOCFlDkVMmSwKBIASpMyv9D39dDJwQsociipl8vYHACtSpgHdDJwEn11J22oo+IT645dMFgUCQAFSpgHdCTAXFgUCQAFSpl744XkALotFgQBQgJSpEJreJGwC18eiQAAoQMoEAAmLAgEgHykTAPKRMgFAQsoEgHykTACQkDIBIBuLAgFARMoEADsWBQJACikTAAAA/kiZAAAA8EfKBAAAgD9SJgAAAPyRMgEAAOCPlAkAAAB/pEwAAAD4I2UCAADAHykTAAAA/kiZAAAA8EfKBAAAgD9SJgAAAPyRMgEAAOCPlAmM6Lnc/t0fvc9iAo/7v6/b8ux9OgBwJaRMaK27Y02vrN8+sOVeKHA9l1t6I9MFaXbwuCs21F774RLyrmd/uK5pydpOPPaQV5WHlyteNFRRA8DgSJlI+kWhVZf67W2P3ax1+3TKPLzm7xCrWPDZia7XD2z8PQk5anwvTD6I8dqjKdMUYH576jYCaq53lz3kVWVwH8rNByhqADgHUiaSPr3qvpP/drb7vjZr+9gw5/5vUihQhgXh/KJDWts4mEyZ2mt//79LWDGl7Cqs9e6wh5yqVB9W1L+oAeAcSJlIkqKQNTrFtg+ngeCeIplAFTMjGwWGSDfH+/t7KmWqr90vZQZPvS1rvZfvwVqVAttQ5ghFDQDnQMpEPtOAUcb2sZAZ3okiL0RPIjz9+vtn/ihW+LB+KdOYlJqy1rt2D9aqFGQOZQ5Z1AAwFFImsqVH9sq2D86Wq6JFLAEURZPslClcu1vKtCallqz1rt6DT8q0Ft3IRQ0AYyFlIps1ctm2f3fmxjvuFJOZscyTfHl2yhRe6JUyh57ELb+NMVp6mVW53/lvw92SLMtYOgBgjZR5JYonAu0U9PzW3ta4/ftaIutwgqeumpsVU096lCozMInX7pUybZO4Q7cT0x4KqjK6ZeRpAsyXA4AaKfNKGqaHyhlTDpmxmKl+xMxfQa13ocolWSkzcu2flHkvfAijcRJ34HZi3kN2VcZ2H9kB8+UAoEfKRIbat7JJs+Xb3W2iwXaaUxFqAo+qTJ9fRsqMX/txMNP8sMeBJ3HLI5lqD1lV+SE+bjP21IMBixoARkTKhJl1ztA8xxjr5v/sk8VteerXmYSygirdmVNm1vxq5tr90ZJP+Wkp9pBdlZuX754iINfvoEUNAGMiZcKm/orczytyOnJVPJOHo9Ivz1nA5Lci3fswNTUZxiypys12783S326GLGoAGBYpExbvftg6lJfxU4lZ/bhqOjOWP5LpzpIyM65ddZJ7I07illy7fg9FVbnZw0peqgUABJAyr6Tyqg7rIGPWoGRBPlFlgHj6SKU760MYc+OIJWXaJ3EHaye5eyiryvUe1kOZimetEjIBQIeUeSVV00ODYcyygKKbzWySMouH8gwpM2MSd6h2kr+H8pS5S42pEMl8OQDYkDKhIvb8z+UW+m/r9utXZYVMdQLQTLOWPZVdfe3iShPDzOxgk7h59Z65h6KqfAVqM97+BitqABgfKRMK8r2Sz+UW+IN1+4/8YTAxHgSSgRwW0jFCMUBmuHbprO13fw6SfCz1HnoclbXllFRl8ItJtAUaizp8gQAwE1Im0lIzrPte2br9W+Z8pO6p3eFBsMCjvDU/gR47S8u1/7ZdHdT2GKOhJnFN9R4MYfaWk1mVq5dutlrHzN3gaebTFUiZACZGykRK4JnXO9tu1Lr99mXWp2qmXiIPQB0TTfxB3JqLsV976BXnfB678doDISyz5eirMvQi4WfK/0k/Omld/DZG5QBAF6RMXNpQY33+hpovvzaKGgDMSJm4svKH6gyN5NMMRQ0AdqRMXFji5wJP7uLjtCOhqAEgBykTl/VcbhceeyL4NENRA0AeUiZwKquVLteN0GOgqAGgDCkTAAAA/kiZAAAA8EfKBAAAgD9SJgAAAPyRMgEAAOCPlAkAAAB/pEwAAAD4I2UCAADAHykTAAAA/kiZAAAA8EfKBAAAgL//7xVOkxU7BmAAAAAASUVORK5CYII=
Note that
data:image/png;base64,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
Answer: 2.28kJ

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