\n A thermodynamic system can exchange energy with its\r\n surroundings in two ways: either through transfer of heat or by doing work on its\r\n surroundings. In other words,\r\n work and heat are the forms of energy that can be transferred across a system's boundary.\n
\r\n\n When a thermodynamic system exchanges energy with its surroundings\r\n either in the form of heat or by performing work on its surroundings,\r\n the system's internal energy is changed.\r\n The first law of thermodynamics is the law that relates the amount of heat transferred and work done with the resultant change in internal energy.
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\r\n The first law of thermodynamics, in essence, is a statement of conservation of energy. It states that the internal energy of a system can be changed in two ways — by transferring heat to or from the system or working on the system. First law of thermodyanmics says that the change in internal energy of a system is equal to the heat transferred to system minus the work done by the system.\r\n $$\\Delta U = \\Delta Q - \\Delta W$$\r\n where \\(\\Delta Q\\) is the supplied heat, \\(\\Delta U\\) is the change in the internal energy of the system, and \\(\\Delta W\\) is the change in the work done by the system\n
\r\n Here, we consider an ideal gas contained in a cylinder-piston assembly.\r\n All surfaces are assumed to be completely frictionless.\r\n The equation of state for the gas can be given as:\r\n $$P V = n R T$$\r\n where \\(P\\) is the pressure, \\(V\\) is the volume, \\(n\\) is the number of moles,\r\n \\(R\\) is the universal gas constant, and \\(T\\) is the temperature.
\r\n Heat can be supplied to the system by means of a heater.\r\n Similarly, heat can be removed by means of a cooler.\r\n Part of the supplied heat goes into changing the internal energy of the system\r\n (by changing the temperature) and the remaining is spent in the form of work done by the system on its surroundings.\r\n
\r\n The change in internal energy is given as —\r\n $$\\Delta U = \\int n C_p dT = n C_p \\Delta T$$\r\n where \\(C_p\\) is the molar specific heat of the gas at constant pressure. It is generally given as:\r\n $$C_p = (2\\eta+3)R/2$$\r\n where \\(\\eta\\) is the atomicity. For monoatomic gases (\\(\\eta =1\\)), \\(C_p\\) is given as\r\n $$C_p = \\frac{5}{2}R$$\r\n while for diatomic gas (\\(\\eta =2\\)), \\(C_p\\) is given as\r\n $$C_p = \\frac{7}{2}R$$\r\n The work done by the system on its surroundings is given as —\r\n $$\\Delta W = \\int P dV = n R \\Delta T$$\r\n Substituting in the first law of thermodynamics gives\r\n $$\\Delta Q = (n C_p + n R)\\Delta T$$\r\n