What is the entropy change when 1 mole of an ideal gas is heated at constant vol

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Question: What is the entropy change when 1 mole of an ideal gas is heated at constant volume?

Options:

Correct Answer: R ln(T2/T1)

Solution:

The change in entropy when heating an ideal gas at constant volume is given by ΔS = nC_v ln(T2/T1). For 1 mole, it simplifies to ΔS = R ln(T2/T1).

What is the entropy change when 1 mole of an ideal gas is heated at constant volume?

What is the entropy change when 1 mole of an ideal gas is heated at constant volume?

Step 1: Understand that entropy (S) is a measure of disorder or randomness in a system.
Step 2: Recognize that we are dealing with 1 mole of an ideal gas.
Step 3: Note that the process is happening at constant volume, meaning the volume of the gas does not change.
Step 4: Identify the formula for the change in entropy (ΔS) when heating an ideal gas at constant volume: ΔS = nC_v ln(T2/T1).
Step 5: Realize that for 1 mole of gas (n = 1), the formula simplifies to ΔS = R ln(T2/T1), where R is the ideal gas constant.
Step 6: Understand that T2 is the final temperature and T1 is the initial temperature in Kelvin.
Step 7: Calculate the change in entropy by plugging in the values of T2 and T1 into the simplified formula.

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