A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. How many moles of gas are there?

검증된 단계별 안내

Step 1: Identify the relevant equation for the problem. To find the number of moles of gas, we use the Ideal Gas Law:

P V = n R T

, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Step 2: Convert the given temperature from Celsius to Kelvin. The temperature in Kelvin is calculated using the formula:

T = T

_C+273.15. For 900°C, this becomes

900 + 273.15

Step 3: Extract the values of pressure (P) and volume (V) from the graph. At point 2, the pressure is 4 atm and the volume is 8 L. These values will be used in the Ideal Gas Law.

Step 4: Use the gas constant R in appropriate units. For pressure in atm and volume in liters, the value of R is

0.0821 L atm / mol K

Step 5: Rearrange the Ideal Gas Law to solve for n (number of moles):

n = P V R T

. Substitute the values for P, V, R, and T into the equation to calculate the number of moles.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas. It is expressed as PV = nRT, where R is the ideal gas constant. This law allows us to calculate the number of moles of gas when the other variables are known, making it essential for solving problems involving gas behavior.

Pressure-Volume Relationship

The pressure-volume relationship of a gas is described by Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if the volume increases, the pressure decreases, and vice versa. Understanding this relationship is crucial for analyzing the graph provided, which illustrates how pressure changes with volume during the gas's transformation.

Thermodynamic Processes

Thermodynamic processes describe the changes in state variables of a system, such as temperature, pressure, and volume. In the context of the question, the graph represents a specific process that the gas undergoes, which can be isothermal, adiabatic, or other types. Identifying the type of process is important for applying the correct equations and understanding how the gas behaves under different conditions.