Joule cycle consists of two constant pressure and two reversible adiabatic or isentropic processes as shown on p - v and T-s diagram in Fig. 5.10 (a) and (b) respectively.
The efficiency of Joule cycle is given by equation (i):
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAA+CAIAAACJLoOwAAAgAElEQVR4nG18+Xcc1dVt/3fvfet9Q/KyyPyFISQG8oAQBwiBJOCEIcSATbABzxOeZMvGlvGAbVmesGV5ErJkWUNPNd55qOqWnPfD+2FXnb4Wb61aWtWt7upb5567zz77nFsN6RjXqXTClEZ55frOL3nb06ZUXKe5jHUhdSFtT/sl65esKZXtaduzru9ymXKdK6+E5dww6QTXeS5TrrgpnHKGSSY0l44rz02pdCFNqWzP2J41pZFOKK+Ul7anu+liLmNhc4xHF9L1jXRM2Nz1jbC5sLnyPBNRJ1lIRVc6Znva9Y3tab/s/JJ1fYOxmVIpz/2yc33jl6ztWV1ov+T9ksc5N4ypTBfalNVIXN/hMKVxfYPvYgymNLDMdz9fPCxxQduzeN/2rPLKlEYXWnmF/yqvcKd4XzohLG/Uxq0uqgvt+tWvKs/pL+yOe1Ne0s/AfJg23B5ujBvGdS4s14WGOXBNfJ3GgYHqQia8w1TCdcpNpr3gOiVbB5OtdSET1saQcNC//JKF0eEfeGl71X1hqLrQTGUYGMwHB3J9BzPZnqEL4mr4AL5OB2xNU0WmwAwpr+COuLvavRRTGWwlnWhwkzGVYD6D2dNkaLoB3Kd0zJSYG2d7Fk5E94Y3hc1hQVMqUyphcxjILztTKl0o5RU3jPxCF5KpJJex7WnpGFNJwjvVTJiMXBhjyEQEZ4c30HJ0fYMDn6fJJh+ECbjOV9iRHNb1ne2ZepASl8J/6QZhNWE5LIbxYxaVV3A7XWh6B3eKmQA8CMulEw2mklR0heXCcqYy/LwplXQsvBPcQ72Q9aMLE9Bk6U3yO3weJzRt8Hf8vHRCecl1mokol7F0TDqmC8lNFuctrlNcAdOGr2ci4iaTjplSYUg46JwcH2+SvbhhuE0CATIfzQGcIFxMNDd0IiznOsc7uAJNKuYVJ/gA3Sn9Oo5GKrrcZLqQqehmIsJ9cp0yleBceZ6KLs7hjMpzv1wIyztJs55YDnTG+oBpyEz4inSMmwzQgc/DysrzTrKw2JlJeAfYgo8lvKM8x+fh0cLmWBZYQAQy5J60QGuTVaGI1jtsB1QhoCMU1oW2pcGwMTDpWGhKUxqmMtixngyFQcJTlWHWSWOFsUIbLlVeQa5htEoqu+PqdBtwcNyJX3awe+jv9aJ2mOQaNyUFOgxFeY5zbjK85CbLZcxNBrMCQ8jE7Xge0RKGpgmjhWJKxVQCuyPq4CcI6ynM4hbwvikfcWdCBr9chLgBCIZpuE7J6Mpz6QStDHgxLRFhuSkruKts6IV1UhuuNFOaqdrccHamMqYyRL4GxW7CdHhN6D6wPgDaL1nbG2BijY+6XtSaQihdE2OCpchV8RInwuadZAGxlGAklzHmBhOpC6k95ybjOoXF67in6YLkFhgwGQ6WgoPDx7FMKbAT4My3pm/cuoS5xzBgOCAGXaSmA1oXin5Xea4cN1bESct6ZaxQmgHc4eMV5TOMqawBQ8Nh6Zws6JcsJoZCvF+yptSgLuRBsHU1T8uOvkUHIB5Lh5Aazo4jypqwci5joBzmA/NEK1J5zlQCcCfQp2vS3NO8Ssf8kgewUKALgYX4mPb625lbew9sYyoJ4Q6W4o96Lg7pRE00KgpkCiVkdvrU8I0bF40R2nCyOyEb+F4DwBQ6aTDi2vGXHWa1Mv2yp0Bae30Q1pZd8dCHRg84WbVuAKCE3dxk7Xie6xQBFn7KdYq1UvtdZetMRMRtyMorHJ9WmC4k/JRwnDwXpocthOUpj7fu2CgNw7IDzUNmA7sDKOhbutDSKWlZuGqV464w1snhw3smJ8eNFcR/cB2EZWF5A24YOg5ZvHjoCSXptnHPrm9MqV3f6kLVrJwTLhHHCFiBQiKGbAh2qVBFp6noRlkTng4YQfaEAIAQTWEjFV1aNwTuK34rhPsQ2W3PGm+MVdppbaWQTDkJjJ6ZvX3txgVpmTZcGaYNFypTtbcylYEFSp1py6TK3n77jd88//TzL/76pZdWffDhX6XOhEq1yaVKtWFSpUeG92jD6hkSRFhx3ghjUZVx1AkbuTBcvnjoKQn0y678V0HMEkkjoQ1x/xAKMLuwHR2YAOlYwtqV3WsiRAd9F2kBCBjWxABY6w+EpB4LIqSA0glbOGOVdQZ/teVIknfs2ji7cFdapjTThuNQmpGr5jLlhsGync7sxbETc7N31q5dk6TNPbs/qy2ea5MLmVjLt2392NSxFC6PS2G5NCgtItJN2EKmJINW2F1/pnjoQ9wvHvrioV/h9UHeqIjtYPWA6gBJgO9IoIA8MGJo3NDuRHvI5elqIftWnhODrDJSp1xhjZXaCFcYZRjG+Yc3XspEJC2zTkqVK82EzJRmmUgqZzeM6zxnHSETLmJt8hPH94+ePyZkIlUqVap0BtMby6wXR4/smZ6eQKKE9BW+D6xvkAXJoGRcvFwhgwC7KXjSJ/GSPJ2+SHkjLSAyFmGF8jzKmoQwNS4zkmsAuDiirEkSQsi1KQjTRWrkVSFT1Ia5QlknjOXWS1VrR+/94y1pGfxdaSZVLmRmrGAqg+lhdxgXf999909zD+7A05XOKk933FimdHb92rn9e7dwnYfyALIB5VXjER8PfJnQgwwNm5b/KuDLFfIsWUqs6VLwoOqLS9bV6wYuD2SnSAh/j/MWHBZODbOC78OyRH7qcMdCl8e3aCZoGuDvIQOROoM/WseFTESNbK++/ttqGWkmZCZVznjCRcoNS0WcyzSXKVOZ0hlj3SxvS5X+8pc/xYmxbOzCCOOR0pmxDHZvtaa3bf04zA8oCajiKtG+0MHxsvxXAcChjL9y84Hap0Pwwb9WkMhQaaLQvUJ3Q1wlTCd+yeHyJkPIxQlSVpqJ6gMmC8hftVakY9KBOHOus1Znbnh497Fje08c37d/7+ZuNMdVAjXij39ZnYkoFV2pMsbjxcV7SdpiLGIq5SZnKs1EnImYi4TxOGfdTzd+sOatPzAecRFfuXzqzTdfBgQpncH3W63pfV9sDjNVxAlEmoq/k+eG4L7yZa17rCAtIYX4rjZL7k9UkrweoAwPhQ5MtDIEGZgyE1HC2lHWbHbud5KFhHco7w1XQJUG65ROaD6kY7fuXmWsu2Xzulu3Lu3audEVMhcRZOdX/vgiU0nKO2nWunPnyo9+8r25B3dy1sllnPBOJqIoayasnbMoZ9HU1MTo+ZHLl07HSfP+/VtTU+ObN33EeESHkMm1b85eHDtBJBKECtmvdKJBSA26MmAstdpOc0DTQ56+AsTDeBuG64DSkQQ/QHZQ9YS1YWhdSBiLRAVQ6YR3kMFCyMM8kZuT42MOcE1yfzpPeEfp7K23XlE6i6J5IZNcREiUPt38EddplDWzvM1F/NJLq+bn7kqV4kdzGaeim4ouYzGirjbcGMFYdOXyqf17t/z+98/F8QLFWCGT8evnz539kuscgSHUxk1pGmRxQEpl/SBIEo8kxCd/J9gBmg/mr8YrkqsoLyMyQ5QDFomyZuin5KEAfdx5ZVaTwQqJ6MLKMBz+i3Mso1zGmYiqmKxTfNI58c47b3ARS5VmeVuZHBf8cP07+BXGulzEzzz7xIPZ20pn+EVcWXle9FzRc64wOLhIEGMP7NsqZMJ4xFg3Z52ctS+OnRgdPQ7uT5kX0tcBnyGaiJNBSHwUJQgiCOvJi8mvH8GrAGpsIOK7QTVHmVLlMu6mi4TIZPEB1OgUsJ7wDtZ7qzubsDZZmTCdlggdBFaw4KmTQ7t3fZqzzvj46IXR40zEqehynW74/IOEtVPeRZxcvfrZTmdWm3y+de/s+WPnLhw/O3psdGyEsThJ2xfHTo5fvzB6fuTypVNjF0YmJsYmJsauXjkzOXkN4C5VeuXyqcuXTpKbA9zBZ7jOGwTQj2gstU1D+WmF0kLiFHFQCrlIqapZXHaE6cpzXdO7VHThQdxkQqdx3qKSE0k08ERy6ihrJryTsHYmIvp8pWHptAKTepIGs6hTaG04efyJH05PT3ARz8/dXbt2zc3bl7A4Ptm4VlqmvUDu89xzT7Va076sdD3ft73/W/plV/a9L03Z9/3lsr9c9JZcb8lZL3LW6XRmFxenwCa1yUdHj58/f6zWOHMIEtKJhEcVjyQ3JOig4Am/DtXKkNEDMaDeVLE0CKewuymV9cKX2ntZFMqX2gYxVhdSOaZ0BnAEAxtQlwDfwWEgimE+gO8DWH/UzTFbtAKEzXMZj98ce//9N8fHR4VMOp3ZZ599cnFxypea8WjT5x/6UmuTW8fTrPXmmy+Pj4/C7sLmlFT2lpwvddm3Zd/ivsq+NZYx1hUy0YHmevHK6QsXv0JQpUxVOpGJRDrRIG6H8Zm6MkdpPdL0EDSId4fpeIj+YbB9sPDtwsLk3IM79+/fYqzrCulKTagFzVqqtNt9wEUcJ4tRNL/YmelE85ViAzvC/WvPhUqM6QHxx8TgIEAPoZmrNBNRwjsIfYx1rRcLC5NnzwwrnQmZHNy/zXoBImi96C95V0jrBeV3uMGyb8q+7S05xqM4XuCiigdVRNWDws6FiycuXjkNfAd5l04A66UTDf1oWSvEX3h0mPKQhBtm/2E6WoFVrTFcGx/ds3fz+/948/XXf7dn92eXL500lmkvgDlVSumF0lmcLGqdb/r8w3NfH33hd8/s2v35pq3rKWYmvNNNF7vpIqgkXqaiixWQiQgHWZ/cHC+Ja3KdgmVrk585dejMqUNzD+5Yx9vtmUNDO8q+tY77UlvHrReukK4W2mj141+MR59uXLtzx4bf/nbVhk/eX7/uHW1yLmLtOIHH8Jdf3Lh1iZIm4pGV3bEYEf1zGZPnwt9pJghnqgLIkiVhhASD76a+N25dsj39s5//YGJizFiW5W3rOAZHSZPyXMgkiuYZ63a7D27fvvz+B2uEzsZvjlF9HA4e5604b6EeSXZEPMhlnLA2ITultZg22L1iOzKBQZN40Tpe9IyxrNt9MHx4V9EzvtRIZa0XeBmKg7qQRc9YL5K02WnPTk5ePzS0g/Ho3r0biAqmEOSFIycP3rt/E5IcCUQoE+pCN+jeMD6KsTAowCTk5qGDk+pPaE6Lo4IpxxPW/s/v/RvUIqCnqiWXKs9UKeMR2LTS2WuvvXjxymlAdmXfuhgyAI06a4VrY+SIt4RFwChMUsgjjWXWcVjWl9oVsuiZOFo4cXy/LzXeweFLbSxbUV3Bv4qecYX8dOPayclr+EoVw3qDnP/w0T3Ts7eoZwKtBtKJXKa60A1kehACUVk2QRcDXDjEOF3IYsmG43P1aiDkgS+7npGOfX3uy+HDu6wXnc7szfExIRNlcq7T+/N3Jm5fnr5/69t743fuXEnSJuNRt/vgxz/9PuORdVzpbHFxivGIYiaMTqhSxV6ZQJYSMkmzllApeXo4SUSTKnHKsLrppfKwTVvX21KTDkpFiBXKfnW/XlgvXnjhV2nWKnomSZra5L7Utm6Qcn139PiBOO9Qiw4qurrQXOemNA0whIS14S8Ja9ugc4Zq86FC4PsWaxBQ6OqQEEI8xiot27Rlfbt9X5t8cvLagb1b70/fFDo1pUpFt92da3but7uzrdZ0mrWMZde+Obtn92dCJjnrTE9P/HrVL5C5VIkS78R5qx3Po7umCp4yUTpDfBMykTobpLs1KaomqVoiKVKYug5VUa9/bvwHcjQduFEo+YFuYB24Qt64NvrKK//HFbLdmtmyed177/3ZFdL3rF8uioelX/Jf7NtmSoM5wGRQW4fyqgE9BKI2sQWAQEjhKS1yPaPrmFP2bZI2bSHDQjOFflOqqZmJP7318u3blyEB7tj+SZwsasdJhecmkzYHn4njhfXr3vny6Bfw96tXzqx65nGlKz4T561OstCO5uZb95qd+wOUlwmcHSyFy1jUzk6VcZzD+mGXCwrTMPTZ0WOL7ZmwOrZCfUIoAp4ImbzzzhtbNq8zlhU9027P7Nq5UemsXKpaiUxhjhzbj74uavDyS57axxqUGeL2pGOp6MK/MCW87tgiL85FhOxg44Z/rF/3jrWcsAXrg2IvxBaEMphy65b1LqCh0jFpc+A741GSNHPWUTo7fGjnoaEdP/7p97O8jZYmeHo7np9rTs01pyp/N5k0WZa3u90Hp04OgdIRlCMA4OsUD1AAgqiLrikMY3bh7sVLJ3GzZH3QaGTv4AJFzyAUx8miVGnZt0XPPLh/+7XXXlQ6c6XxS94vF9KJo1/ul06ErV2u76QTqYh1oRsh2ZKODX/5RTuau3jl9HzrnrQMi2CuOTXfnEryFsQpbZmxLM1aXMTbtn5svQgzLyJC0FdNqRBRr1w+devWpTOnDskwrdepNBnjUZI2AdOQO8YujOzfu+UHj/3H/NxdMlyUNdvRXDuaa8fzVBfMeMRYd/eOjW+88TshEyEH5qY1QeQnE9GgeGSY8go9s0h2Dhza8e30DSr/hr5PcatiO45TbMvytvVi69aPreO21K7vpBVbtm/oJE0EUvyljiO804AKCgdBRWLN23+8eOnkuQvHMdvSsVu3Lg0d2H5oaMfWLes/37hWqdRY5gpZlOajD/9mDEMYBPl1hRQ2dz2D/Nv2dNEzRWnwFWMZVwmMXkmPOs1E1I7mSGxBGsJF3G7PSJVCD8hE1OrOdtPFB/N3m817SdJM0mbOuznrMNadmBj75J9/B8rD3Gjzg/VJ1cpEJFTOeKINFypHXanoOaVzbTPn2ZkzQwsLk5BorBfGVukLVVSquOq4sUzr3JTmztTE0PCeHK0GTpQ9v3nTeqVZ2fe+5whYgDM0E42sFkKRaPUeFrv2fC5NfvP2FXRmmVKNnj+2d/dne3Z+enDf1iOHd8GC1ouyb7dsXgd2ePnSyVMnh5CMnB89zk02PjF26Mju3Xs2XRw7MfLlviPDu4cObD90YMfQ4Z1fnT507Pj+oeFdR47tGxredfLM8O4vNu07uG3Xns/37tu6ZfO6zZs+2rP7sx3bP/l049oNn3/Q6s4KnbWjufGbY4cP7zxz6tCpk0NnTh1Os1YcL+Ss8+231//58XtZ3mY8YjLJRUxaPISdKGseHzmwb/+206eGR44dOHpk78ixA1+NDJ0+NTx24avr185N3LwwMTE6OXnl7t1v7t79Znp6Ymbm5uLiFMIJydTGMl9q8Mjekiv6HvZ1pXGlKXs+y7pJ2u4vlVAu4el0QIx0fddwfTOQn0w237o38tVB6dilq2d43atlvFh6WPT6bvlfPe8laIwvdVGo7dv+6Zzwpe4tuaXlYvlfZVFUkQA4oAupTd7rO2gaxjJbKq5SagJwfSNNnvCO9qJc9rancUvOVfmL9oLJSnbf8PkHr7324m9/u2r16mc3fPJ+zjqMRznrLCxMfnn0C6nSnHW27dzw5zWv/O3dN55/adWnmz+StdKrC5nxCNW7onSt9myzOTM9dfPu3evfXD17Y2L00qXjI8f2fDVy4NCBHVu3rEf0+tu7b/xlzatv/e21P7318l/WvPrCC79+5tknfv7fj/3i8cd++OPv/a9//58vvbDq+eeefuK/f/jUEz958vEfv/jiqpdffv611156660//OUvr9z+dhztG4i3RGEbQC4sTPBi6Zi07OSZ4YHwbZnxwhZSO24KoX2Fbq3W9Inj+63jsCliDnI81zfC5ogQgBdtcqxc+WghCSEEsFAdIqbaccVnTJaKbidZ6CQLad5KsxZqC1KlXMTW8ZFj+9588+UkbXIRD2hCXfSgSIvyKXVqoIHUOmm9NJ45n88v3pmfu0tZVdEb5Ik4CRUxX+pe3/dKV3rdK0yvdEVplWbWK8YTxuI4bqJXiVqmBjiDSA36CHUbmLj7i01hP9NAEO5rUwgsNNIxMJqBskE5V9+mvBvHC0m8CGsKmZhCkNyGgMxNRnEyYe0sa3e7D6JoPo4XGI8ol660XxFxEYP2kNgNXbCq9QSFjkGdti5LWSetk9YrqXI0DXCRKp0bzx7M3Txz6gCkAhi97FtbN9rjjuBeiK5VotR3xZJ3PWsK43tOa35oaJexoug5V1pQeFsO9oGY0vjlokGKru3rKmtl7U6ycH/+DmVrdqmm8EsGH9Oe20LaUptC2VL7vimWnO9bW0hXVpMEQNy+Y8PZM8PPPvvkua+P7tyxwZdaWxZW+JTnXCY57zIR3528dubM8LZt64eGtm7Z8uHcwm2pB8lqpc+wNpOxNFl12Fw5JnSa8S5XKa8V/LD2jTkAY9ZeSMtModC1oR1XOodEs++LTcpkttTac1MIW2rthSm1X3K2Z3ShdKFcz/i+saWypfJ9q72SmkkrtNe2NL60Zd9LlX+68UMhs95SUSwV1Ejq+g7qmF/yDRIAqHeO8kPag0GUluoYRHXMd9pjyNmrzgCdfbpx7eFDO7XJc9aRKoV4ZIPNG1zEyFdBYDZseJfLzrXrXzufSx3DcMB3HHHeIu5Lq6GyLCayri6Rv1PhkPptKqHcMqUzxqNvrn499+CODDpEah5pwv0e1Dly+erX+w9uHz68Z/jQnqH9O9Osow13hSn7vug5xuKvTx/xPQej03YanPgl36CKDCLPQNo2GUQ+mB7FDZKIcXskSVK+SpIytW4Jmz/2o/+amblJapQpxCNJoGM566RZC7hhHV/z11e5jOJ0QZlU24wMih1lcd5qR3MQgUmXJ/WGXg7ksLrat6K/o+pzchx87L33/pxmLVUXZoMSvKXea+ywANcY+erg1PTEf33/3xcW7q1e/RupcuskmlJ9abXhh4Z29ZdL2nkDlYYE4QYCIJWGTangKUg+E97pRHOUdmNPF4gw+raqgolOMUqwUpieqaQdzd27f/OZZ59AA9vcgzudzqy0ecLa3GTfjJ+/cu3s1evnxq+ffzB7G+h/9cqZv//9zSzvZFkbVeMVohj+kkEr1l+XljBDlCjRv6jLIyzJcpMJlSIJWr/uHaUzZXIb7JlSnledw05Cvw3ryffn77z73pvgi760vrRU7y56bsMna8t+pZGF25LQytGw9U44X29HggBExS30baGaDPtiZKLeLUaLF3MGT8TS4To9PnLg6NE9qOSdPTP8xJM/ynkXWf5iZ+b+/J35xanp6YnFxSkQmD//afX49Qs5i7Zv2yBVzkUVG1PRbUdz3XQxypqoRIdVb6Lq1MNETU4rpoTS0WpFOmYsy1ln186NlUxNBZna34EVcd6RVpDdlecXxk6Mnh9RmiFQw98xAUXP7d+7LWOR7dniYQmj06ZJ13cNqoISUmMOyP3J9KiT0ZuhbkerUtg8zluAHdc3Ce+8+/6bJ0YOQDh1Tjz9q593k0UUuOFQwuaMdaEmzj2489QvfzI5OW4sP3rkCyEzLqqcDtE+yprddLEdzVF9lSRf2JTcGQs0hBqUWIXOpGXS5NJkXCXSZMbzmfu3Tp06pC2TNjelMoUwhVCOac+r/unSVrtECqW90J7bUr3+59XN1oyxYmLikvVKaeZ7zvds0XdF3x0c2rXQnAGDFJbD9LTHqkGlJSplhbbmJiPqWhE+3onzFr0TKu+4FK93UCrPU9FNWSdJm7D7vXs37t27oYOogAngIkaPVZq12u2ZJF6UKh0+vEubXNW6bpy3uuliJ1lox/MguytawwgtQ1CqZPdaDb43c/PC6PErl099c/Xr+/dvCZlkvMtNduvu1ZGTB5Xn0ubocazIohf1PiaDExBoV0jOopdeWpWzyDr5zDNPcpG6wvhetRHD9uyevVu7aYsbFmXthEdIl2B3v+QbfsnCU4iHkIYOI5K2ThVXCCBoCQoLs65vqIpPvoy8yRWy3Z5Z99Hbx7/cy1XySF27kOj1sY6jWgY9fejAdqUyYxlBNvrlQGlg8ZCYUzcHVVZDkGEq0V58uP6dyclrq1c/OzEx9unGtVzEUmfcZNP3b41d/AqJnlTpzMzNp5/+GewebtO2PQudQKp05Ni+v675Q7s9W5Tuued+WeViTtIemP0HdyY8kk4krAvNHfkqyk8NE3RVoIpNfS+QEBLWNo92JiEUUylZBZsusJZpIist3gukrGnaSpKm9px2E4DPAGQQ34xlXMRcxFNT48iJqBIJoGvH83HeImsSOwy7Nnjd5ARCTHMQZc2RY/u2bf04y9vGMqlSaTJusqvXz42cPChsbgphHb9378avV/0Cei8qFbrQxVJhykG1x5eai5jxuCjdk0/9lLGYi1QZDh3Y9d3O3ZsS1lVewdlpUxU2EDds0OcV9sZQuQM3Y+otllUQrvdIpnWzHKWgqt53OagO1gYFj7RBa4IplS012tuo8sl4DGbJWFfpDHw8Fd2EtSmjRgAn1kgHC/KmsPxNxcLnnnsKXV2gWLD79YkLY5dPQs0H7/rF449ZL6RKpR20lCqvsAjKvkWV1ZfWWPH666u14dYrW5j6QQPu6PEDXOegoblMQUbRz8113kDx2gSbvsKGPZgbHhT2kZGJiUcmvEP0BlejPkVtK/SAgKNtJQITL8rydpa3q50SjmuTA3nQcKHq7U5x3qpoVdjxG9SsqcY9MDoV+UzGddqJ5n/w2H/gskImZd9KnUmTX7l29uSZYXzXFTJOFp9//mm0Md26e230wldXr4+ePT8y15x2hUyz1uLiVBTNLz0s+sslpMf+clmUruwXwnLYeuuOjdiHVu3RqffrAHAatqczEYUiDLVs0JtEFs2jm1SpCoNMioo7Vd2j3g1D2qSpN+QhiSfdDQBC7A1UCtwJzk7xHKE1zlthgxhhDlU5qDEYQRXvJ7wzOjby2ecfaJN3OrMH92/7yc/+dzdZYCo5cWoI/o5RzbfuPffC06DCre7snclrUzMT126MTs1MGMs67dlvv73+zdWvr187d+nK12fOHTs/euLchRNnR0duT15DSdaUaseujdxktNcbQnwiYqB/A45JPJL2gwHECdZ1vY+Cquw26NaDdWB9ILuud/7ZehMsJvK7BUxdSHTFUMkfARl+TQQpYe12NAcqiUrIoCZcu3OoDVD2hJcD+IsAAAdmSURBVPkQNr/77fUnf/Wzd9/9UxTNoyT7m988lfEu1+mBQzsmp8axsITNb929+m//+T+kZUSmkQaaUkERw/K1Xigvw80ktlc5onRsx66NSLvAZJCsdtPWwN8Ji3XdGWCCDfNhlQvlx7B9FShEyQji2IpsgAg+6WVkcdwn6c/gIbga7R/j9b4DkHc05oVkhvyUU9c8NQA/OiXKc4RTLuLp6Ynp6Qlpc26yoeFdd6euq3o/f5Q255pTWLg0+KoTvdZfQSiVk3jiBmKvLgZl/c+3rJOO0ZM+oL9nIsEcNMLGdspdbdCbF2q2NEN+2VH9GssC1oSB4O/UBkIzRLSdZBw4FOwO2KF0F/+CIbACQi1sEC1rsZfXHb+DMKvTqv89iL22EEIm7fb9N9743eFDOzvRHNfp0eP77k5dr+q9joEH66BjiQZclAaNlW+//fpLL63669tv/O6V5+/em0CVHN04upCuZ/bs3eyXKh0YtsZjJao+PQIKXfcDEzKEJCccRLj6bNAgRhKbDfoPiKrLcD95Xf4mVRKrmGwkBruTqrw/5DMJ71BBOBQDqHc+VGzognipTC5V2mpNf3v32tTUuLR5LuOhw7tmHtzG7IZ1bUJLcpeiNEXPzMzcFDL5219fm75/e745E+cd0HzXHzyrZ8v2f5KcSSIwNn6Y0jQAoGHApHzVBP2Otm6zdjWDxBDDpUCG+66KYOpGD/noowVwP5SFkUwI8+l6tx9TSas7i7oH/oaGpobsFVcIRYIQ9ym9Ik14x66NdyavEQsgf/LLLnRK16/4e9Ez2uSrnnk8yzvYbonHn/jSUCPfls3ryjp3Rb8YPe3J9mzVtxT6IFmEsL4CuKAH2NRtGhgW0Uq4oesbWC3cBEvVK4qoRGDQ30uClKqfhUETgEIgFIJu1qxE4CBFCtXHkLDT3KyofoD44qXt6a9OHzp34TjG/P8NTpb2DJXaFdJ7eerk0Jq3XnWFQr0Q0lhvyRP679n9WVlrkOTvmUiqunZVhQlasVfgA5U4VPCgMbystKd69KZUIIW0MGmtyHqnEiYS4QF3ojwHn6HPhMIhwTSQveozrTMjHnRchZASBlXKnlZUP3iw2awdzx85tpfXe1lJBFbBTk84KMqZrpBr164Zv35eG3779tW/rXn9q5EhVxhfGuwAKft2aP/23pInuQaCMPDdlKYh6i0GoSgWTruqd4LRQR+j9ISEX3RYhvBNqmk4tcQpcX1SmMM7FMGWJVy2an5n7UfS1LC1uKYuYUvwI8Sm7onjQe0bsP7Gm7/nOpWm2jWAWw7UYI3vIvdO09bTT//MOSFk1m4/yPPo1VdeVJpZJ5DQSpXu2f2Z9YIsbkrDDctEgmdkNUhUMkHFDnMQGoJGAN5CuRIlihgrol94tRC+qMAG8KF0F6FSPfpgIEKPUG+BCk9NejzoQAn5IjVHUu0sBByKBCp4Ysqly6e+vXdDBhvbKGUhZkE4gz1pk5PX0Pl0+/bVMyeHtea+NNBC5ufujl0YcYWExgBlJsraUdZOWFcXukGQaoO9Bsh9ZP0cGF73att6sw8mBk5a6do2hz+iDkXshWIsXTZcv6HIQ6sBvwsiT/bNRNSO5yG+V2S/boLkgx68Ck/Q27wCYcKoGy4p3GOUNT9Y9zaq3irYZk8CHzm+6xuUKm1PS8MW27PXb1xUTio8qUZlptC/eeHXGY9NoW1hjJe+53xpcx61o/mEdXQhGwgv/NEWZBc8JUYGhWBSH1fknPgXSB7yHcIiitKIAWGA1fVTNsKdeeFiGlB1k6GyCqlgxdYZkihYvf2MnB0npJuGyjClWhQh2vH8mXNHE9bWwYNY6DwETGx3ETbnJj94ePcnn324/+DOVMTC8nZ3YWh4T5J3lVemLvv50qIwAomUm6xR8eJ6swR5ogjqTbTQaEFQqETVG2Mi65A8uYJokoRAiRWsDN+kK4d6FrkqNBzMKyW3Ic6EuERFj0EBxGTcZJ1kgbSHR7imTmnx0ZUJ9EzwCEwCnJo+5QQj1QNLdZ7LtGpHtdx6gWK9sUzIBHKI7ekGGCG8FdanlNrVzwQkOkUEkeYgZOKmVKze0F4l5cHDDEJfto92HuBHZf0oH7xDng6RCwpElDUrUSygLsQgVya09V9aCiu+FaZUqnpq4eCRFITA5PiUEwmbA2npUZH05LbwAalcZydPHvjyyz1Jtmg843IgGjZCW2CGsQIIUqjiaoJSlK4f0IP5AC8EwwkzFCqkwL60/T6EMkB5heY1faS8kXgORtXqzrbjedpMTAlReEIaZ+jLVKKi+aCcVgZlbhk02EAW1oWExEhIQLFKF1J7hf1K9JhC2B0EptmZfeut1a/98fnbd8ZcyYzPFjsz8MiGDB4YFeb0IMvwMhImQ6F4xUF+iilVtY4YJlYEkSooUUnHyO60jMJcH4YAlaTsaYXF+aMq2MDuEAZ0pkzOVcLrAqysm5NCu6u6ohC+xE/Tsg4nSReS6ZSbnJtcWIbHDOJAPTYT8enTB48c2RnFs67kxmWp6ArLbM/8PzhJh6a9Xsz8AAAAAElFTkSuQmCC)
We know that for reversible adiabatic or isentropic expansion 2 – 3,
![](data:image/png;base64,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)
and for reversible adiabatic or isentropic compression 4 – 1,
![](data:image/png;base64,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)
From equations (ii) and (iii),
![](data:image/png;base64,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)
Now equation (i) may be written as
![](data:image/png;base64,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)
Notes:
1. The efficiency of the Joule's cycle is lower than Carnot efficiency. The reason is that all the heat is not taken in at the highest temperature and rejected at the lowest temperature.
2. The cycle is not thermodynamically reversible, because there is no re-generator to provide a constant temperature during heating and cooling at constant pressure.
3. The reversed Joule cycle is known as Bell-coleman cycle, and is applied to refrigerators, where air is used as a refrigerant.
We know that for reversible adiabatic or isentropic expansion 2 – 3,
and for reversible adiabatic or isentropic compression 4 – 1,
From equations (ii) and (iii),
Now equation (i) may be written as
Notes:
1. The efficiency of the Joule's cycle is lower than Carnot efficiency. The reason is that all the heat is not taken in at the highest temperature and rejected at the lowest temperature.
2. The cycle is not thermodynamically reversible, because there is no re-generator to provide a constant temperature during heating and cooling at constant pressure.
3. The reversed Joule cycle is known as Bell-coleman cycle, and is applied to refrigerators, where air is used as a refrigerant.
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