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Calculate the internal energy and entropy change for a gas that undergoes an isothermal expansion from 2.0 L to 3.0 L at a constant temperature of 300 K.

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To calculate the internal energy change and entropy change for an isothermal expansion, we need to consider the following:1. Internal energy change  U  for an ideal gas during an isothermal process is zero. This is because the temperature remains constant, and the internal energy of an ideal gas depends only on its temperature. Therefore, U = 0.2. To calculate the entropy change  S , we can use the formula for an isothermal expansion of an ideal gas:S = n * R * ln V2/V1 Here, n is the number of moles of the gas, R is the ideal gas constant  8.314 J/molK , V1 is the initial volume  2.0 L , and V2 is the final volume  3.0 L .However, we don't have the number of moles  n  given in the problem. To proceed, we can express the entropy change in terms of the initial and final pressures  P1 and P2  using the ideal gas law:PV = nRTRearranging for n, we get:n = PV/RTSubstituting this expression for n in the entropy change formula, we get:S =  P1V1/RT  * R * ln V2/V1 Since R and T are constants, we can simplify the expression:S =  P1V1  * ln V2/V1  / TNow, we still don't have the pressures P1 and P2, so we cannot calculate the exact numerical value for S. However, we have the expression for the entropy change in terms of the initial and final pressures:S =  P1V1  * ln V2/V1  / TIn conclusion, the internal energy change  U  for an isothermal expansion is 0, and the entropy change  S  can be expressed as:S =  P1V1  * ln V2/V1  / T

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