0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are temperature T₁?

검증된 단계별 안내

Step 1: Identify the given values for state A from the graph. The pressure (Pₐ) is 8.00 atm, the volume (Vₐ) is 2.00 L, and the number of moles (n) is 0.0050 mol. The temperature (Tₐ) needs to be calculated.

Step 2: Recall the ideal gas law, which is expressed as:

P V = n R T

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

Step 3: Rearrange the ideal gas law to solve for temperature T:

T = \frac{P V}{n R}

. Substitute the known values: Pₐ = 8.00 atm, Vₐ = 2.00 L, n = 0.0050 mol, and R = 0.0821 L·atm/(mol·K).

Step 4: Ensure all units are consistent. The pressure is in atm, the volume is in liters, the number of moles is in mol, and the gas constant R is in L·atm/(mol·K). No unit conversions are needed.

Step 5: Plug the values into the formula and simplify to find Tₐ. The calculation involves multiplying Pₐ and Vₐ, then dividing by the product of n and R. This will yield the temperature Tₐ in Kelvin.

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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. Here, 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 fundamental for understanding the behavior of gases under various conditions and is essential for calculating unknown variables in gas-related problems.

Thermodynamic Processes

Thermodynamic processes describe how a gas changes state, including isothermal (constant temperature), isobaric (constant pressure), and isochoric (constant volume) processes. Each process has distinct characteristics and equations governing the relationships between pressure, volume, and temperature. Understanding these processes is crucial for analyzing the transitions between states in the given problem.

Pressure-Volume (P-V) Diagram

A Pressure-Volume (P-V) diagram visually represents the relationship between the pressure and volume of a gas during various thermodynamic processes. Points on the graph indicate specific states of the gas, while the curves represent the transitions between these states. Analyzing the P-V diagram helps in understanding how the gas behaves under different conditions, which is vital for solving the problem presented.