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 from temperature T1 to T2?

Options:

Correct Answer: R ln(T2/T1)

Solution:

The change in entropy at constant volume is given by ΔS = nC_v ln(T2/T1). For 1 mole, ΔS = R ln(T2/T1).

What is the entropy change when 1 mole of an ideal gas is heated at constant volume from temperature T1 to T2?

What is the entropy change when 1 mole of an ideal gas is heated at constant volume from temperature T1 to T2?

Step 1: Understand that we are dealing with an ideal gas and we want to find the change in entropy (ΔS) when it is heated.
Step 2: Remember that the formula for change in entropy at constant volume is ΔS = nC_v ln(T2/T1).
Step 3: Identify that 'n' is the number of moles of gas, which is given as 1 mole in this case.
Step 4: Recognize that C_v is the molar heat capacity at constant volume. For an ideal gas, C_v can be expressed in terms of the gas constant R.
Step 5: For 1 mole of an ideal gas, we can use the relation C_v = R for a monatomic ideal gas, or C_v = (3/2)R for a diatomic ideal gas, but in general, we can simplify to ΔS = R ln(T2/T1) for 1 mole.
Step 6: Substitute n = 1 into the formula: ΔS = R ln(T2/T1).
Step 7: This gives us the final expression for the change in entropy when heating 1 mole of an ideal gas at constant volume from temperature T1 to T2.

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