A sample of a monatomic ideal gas contains (mathrm{N}) atoms. You want to compress the gas slowly

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A sample of a monatomic ideal gas contains \(\mathrm{N}\) atoms. You want to compress the gas slowly to one-fourth of its original volume.

(a) By what factor must you change the absolute temperature of the sample in order to increase its entropy by \(3 N\) ?

(b) For the process in part \(a\), by what factor does the root-mean-square speed of the gas particles change?

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