FIGURE CP19.80 shows a thermodynamic process followed by 0.015 mol of hydrogen. How much heat energy is transferred to the gas?

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Analyze the given problem: The problem involves a thermodynamic process for 0.015 mol of hydrogen gas. To determine the heat energy transferred, we need to use the first law of thermodynamics, which states: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat energy transferred, and W is the work done by the gas.

Determine the type of thermodynamic process shown in FIGURE CP19.80 (e.g., isothermal, isobaric, isochoric, or adiabatic). Each process has specific characteristics that affect how heat energy is calculated. For example, in an isochoric process, W = 0, so Q = ΔU. In an isothermal process, ΔU = 0, so Q = W.

Calculate the work done (W) by the gas during the process. For example, if the process involves a pressure-volume change, use the formula: W = ∫ P dV. If the process is isothermal for an ideal gas, W can also be calculated using: W = nRT ln(Vf/Vi), where n is the number of moles, R is the ideal gas constant, T is the temperature, and Vf and Vi are the final and initial volumes, respectively.

Calculate the change in internal energy (ΔU) of the gas. For a diatomic gas like hydrogen, the internal energy is related to temperature by the formula: ΔU = (f/2) nRΔT, where f is the degrees of freedom (f = 5 for diatomic gases at room temperature), n is the number of moles, R is the ideal gas constant, and ΔT is the change in temperature.

Combine the results from the previous steps to solve for Q using the first law of thermodynamics: Q = ΔU + W. Substitute the values of ΔU and W into this equation to find the heat energy transferred to the gas.

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주요 개념

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Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It encompasses laws that describe how energy is transferred and transformed in physical systems. Understanding thermodynamic processes is essential for analyzing how heat energy is transferred to or from a gas, as in the case of the hydrogen mentioned in the question.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or system to another due to a temperature difference. It can occur through conduction, convection, or radiation. In the context of the question, calculating the heat energy transferred to the hydrogen gas requires understanding the specific process it undergoes and the conditions affecting heat exchange.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law is crucial for determining the state of the hydrogen gas and calculating the heat energy transferred during the thermodynamic process.