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Ch 19: The First Law of Thermodynamics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 19: The First Law of ThermodynamicsProblema 2
Capitolo 19, Problema 2

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is 27.027.0°C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done 2.40×1032.40\(\times\)10^3 J of work.

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Convert the initial temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary because the ideal gas law calculations require temperature in Kelvin.
Use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). Since the problem does not mention heat exchange, assume it is an adiabatic process where Q = 0, thus ΔU = -W.
Recall that for an ideal gas, the change in internal energy (ΔU) can also be expressed as ΔU = n * C_v * ΔT, where n is the number of moles, C_v is the molar specific heat at constant volume, and ΔT is the change in temperature.
Rearrange the equation ΔU = n * C_v * ΔT to solve for the final temperature (T_f). Substitute ΔU = -W, n = 6 moles, and the given work done by the gas (W = 2.40 * 10^3 J).
Calculate the final temperature (T_f) in Kelvin using the rearranged equation. Finally, if needed, convert the final temperature back to Celsius by subtracting 273.15 from the Kelvin temperature.

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Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics, expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. It describes the relationship between these variables for an ideal gas, assuming no interactions between molecules and that the gas occupies no volume.
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First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or converted. In the context of gases, it is often expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. This principle helps in calculating changes in temperature when work is done.
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Work Done by a Gas

Work done by a gas during expansion or compression is given by W = PΔV, where P is the constant pressure and ΔV is the change in volume. In thermodynamic processes, work is a form of energy transfer, and understanding how it affects the system's internal energy and temperature is crucial for solving problems involving gas expansion.
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