Calculate the entropy change when a sample of 30 g of Ne is expanded from 1 L to 10L and simultaneously cooled from 350 K to 300 K. Cv = 3/2R

To calculate the entropy change, we can use the formula:

ΔS = Cv * ln(T2/T1) + R * ln(V2/V1)

Given that the sample of Ne is expanded from 1 L to 10 L, we have V1 = 1 L and V2 = 10 L.

The sample is also cooled from 350 K to 300 K, so T1 = 350 K and T2 = 300 K.

Since Cv = 3/2R, we can substitute this value into the formula:

ΔS = (3/2R) * ln(300/350) + R * ln(10/1)

Now, we can calculate the entropy change step by step:

Step 1: Calculate the natural logarithm of the temperature ratio: ln(300/350) ≈ -0.1823

Step 2: Calculate the natural logarithm of the volume ratio: ln(10/1) ≈ 2.3026

Step 3: Substitute the values into the formula: ΔS = (3/2R) * (-0.1823) + R * (2.3026)

Step 4: Simplify the equation: ΔS = (-0.2735R) + (2.3026R)

Step 5: Combine like terms: ΔS = 2.0291R

Therefore, the entropy change when the sample of Ne is expanded from 1 L to 10 L and cooled from 350 K to 300 K is approximately 2.0291 times the gas constant (R).