# What is the entropy change for the isothermal expansion of #"0.75 g"# of #"He"# from #"5.0 L"# to #"12.5 L"#?

I assume you aren't given an equation and have to derive it.

You should get to know this pretty well. The righthand side is a derivative we are familiar with. The ideal gas law can then be used.

Now, the derivative is feasible in terms of an equation we know:

This therefore gives:

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The entropy change for the isothermal expansion of 0.75 g of He from 5.0 L to 12.5 L can be calculated using the formula ΔS = nR ln(Vf/Vi), where ΔS is the entropy change, n is the number of moles (n = mass/molar mass), R is the gas constant, and Vi and Vf are the initial and final volumes, respectively.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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