The text in the image discusses a thermodynamic process where two moles of hydrogen gas are heated under constant pressure, with the volume increasing by a factor of 4. The problem asks for the change in entropy, given the universal gas constant $R = 8.31 \, \text{J/mol·K}$.

To solve this, we can use the formula for entropy change during an isobaric (constant pressure) process:

$\Delta S = nR \ln \left(\frac{V_f}{V_i}\right)$

where:

• $n$ is the number of moles of gas,
• $R$ is the gas constant,
• $V_f$ is the final volume,
• $V_i$ is the initial volume.

Given that the volume increases by a factor of 4, $\frac{V_f}{V_i} = 4$.

Now, let's plug the values into the formula:

$\Delta S = 2 \, \text{mol} \times 8.31 \, \text{J/mol·K} \times \ln(4)$

I'll calculate the entropy change for you. math

Given values

n = 2 # moles of hydrogen gas R = 8.31 # J/mol·K, universal gas constant V_ratio = 4 # final volume / initial volume

Calculate entropy change

delta_S = n * R * math.log(V_ratio) delta_SThe change in entropy ($\Delta S$) for the process is approximately $23.04 \, \text{J/K}$.

Would you like any further clarification or details on this calculation? Here are some related questions you might find interesting:

1. How would the entropy change differ if the process occurred at constant temperature instead of constant pressure?
2. What are the implications of a positive entropy change in terms of the spontaneity of the process?
3. How does the entropy change for an ideal gas during an isothermal process?
4. How does the change in entropy relate to the second law of thermodynamics?
5. What other thermodynamic quantities can be used to analyze this process?

Tip: When dealing with entropy change, always be mindful of the type of process (isothermal, isobaric, isochoric, or adiabatic) as it dictates the appropriate formulas for calculation.