19.11
Capacidad Calorífica: Resolución de Problemas
La capacidad calorífica de un gas es la magnitud de energía térmica requerida para elevar la temperatura de una masa unitaria de gas en un grado Celsi…
Considere un cilindro de metal que contiene 160 gramos de gas oxígeno con una masa molar de 16 g/mol en una habitación a 25,0 grados Celsius. El cilindro se mueve y se mantiene fuera de la habitación en un caluroso día de verano.
El gas oxígeno en el cilindro entra en equilibrio con la temperatura ambiente, ya que 600 J de calor se conducen a través de las paredes del cilindro. Ignorando la expansión del cilindro de metal, determine la temperatura de equilibrio.
Para resolver el problema, primero, identifique las cantidades conocidas y desconocidas.
A continuación, el número de moles se puede determinar dividiendo la masa del gas por su masa molar.
Recordemos la ecuación de la capacidad calorífica molar a volumen constante.
El oxígeno es un gas diatómico; sustituyendo el grado de libertad, se puede obtener la ecuación de la capacidad calorífica molar para un gas diatómico ideal a un volumen constante.
Por último, al reorganizar la ecuación y sustituir los valores, se determina que el cambio de temperatura es de 2,88 grados Celsius y la temperatura de equilibrio es de 27,88 grados Celsius.
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Q1: How do you calculate the number of moles from mass and molar mass?
To find the number of moles, divide the mass of the gas by its molar mass. For example, 160 grams of oxygen gas with a molar mass of 16 g/mol yields 10 moles. This calculation is essential for determining heat capacity and temperature changes in gas problems.
Q2: What is the molar heat capacity equation for diatomic gases at constant volume?
The molar heat capacity at constant volume for an ideal diatomic gas depends on its degree of freedom. Oxygen, a diatomic gas, has five degrees of freedom. Using the kinetic theory of an ideal gas, the molar heat capacity equation uses the gas constant and degree of freedom to calculate heat energy required to raise one mole by one degree Celsius.
Q3: How does molecular structure affect a gas's heat capacity?
A gas's heat capacity depends on its molecular structure and degree of freedom. Monatomic gases like helium have three degrees of freedom, while diatomic gases like oxygen have five. The degree of freedom determines how many directions molecules can move, directly affecting the heat energy required to raise temperature.
Q4: What is the difference between heat capacity at constant volume and constant pressure?
Heat capacity at constant volume (CV) measures heat energy needed to raise one mole of gas by one degree Celsius while volume remains fixed. Heat capacity at constant pressure (CP) measures the same for fixed pressure conditions. Both depend on molecular structure, but CP is always greater than CV due to expansion work.
Q5: How do you find the equilibrium temperature when heat is conducted through a cylinder?
Rearrange the molar heat capacity equation to solve for temperature change using the heat conducted, number of moles, and molar heat capacity. For oxygen receiving 600 J of heat, the temperature change is 2.88 degrees Celsius. Add this to the initial temperature to find the equilibrium temperature of 27.88 degrees Celsius.
Q6: Why is the degree of freedom important in heat capacity calculations?
Degree of freedom represents the number of directions a gas molecule can move in a dynamic system. It directly determines the molar heat capacity value through the equation CV = (d/2)R, where d is degree of freedom and R is the gas constant. Different molecular structures have different degrees of freedom, affecting their heat capacity values.
Q7: What steps should you follow to solve a heat capacity problem?
First, identify known and unknown quantities including mass, molar mass, and heat conducted. Calculate moles by dividing mass by molar mass. Determine the gas type and its degree of freedom. Apply the molar heat capacity equation at constant volume, then rearrange to solve for temperature change and equilibrium temperature.