0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are pressure p₂?

검증된 단계별 안내

Step 1: Identify the given data for state B from the diagram: Volume (V_B = 4.00 L) and Temperature (T_B = 620 K). The number of moles of gas is also provided as n = 0.0050 mol.

Step 2: Use the Ideal Gas Law, which is expressed as:

P V = n R T

, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant (R = 0.0821 L·atm/(mol·K)), and T is temperature.

Step 3: Rearrange the Ideal Gas Law to solve for pressure P_B:

P

_B=nRT_BV_B.

Step 4: Substitute the known values into the equation: n = 0.0050 mol, R = 0.0821 L·atm/(mol·K), T_B = 620 K, and V_B = 4.00 L.

Step 5: Perform the calculation using the substituted values to find P_B. Ensure units are consistent throughout the calculation (e.g., L, atm, mol, K).

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주요 개념

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental in understanding the behavior of gases under various conditions and is essential for calculating properties like pressure in different states of a gas.

Pressure-Volume Relationship

The pressure-volume relationship, often described by Boyle's Law, states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This concept is crucial for analyzing processes in the provided graph, particularly when determining pressure at different volumes.

Thermodynamic Processes

Thermodynamic processes describe the changes in state variables of a system, such as pressure, volume, and temperature. Understanding the types of processes (isothermal, adiabatic, etc.) helps in analyzing the transitions between states A, B, and C in the graph, which is key to finding the pressure p₂.