Question

At \( T = 27^\circ C \), \( V_i = 0.4 \, \text{L} \), \( V_f = 0.8 \, \text{L} \), find isothermal work.

Hint:

The isothermal work is calculated using the formula \( W = nRT \ln \frac{V_f}{V_i} \), where \( n \) is the number of moles and \( T \) is the temperature in Kelvin.

Answer 1

Step 1: Understanding the formula for isothermal work.
For an isothermal process, the work done by the gas is given by the formula: \[ W = nRT \ln \frac{V_f}{V_i} \] where: - \( n \) is the number of moles of the gas,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( V_f \) is the final volume, and
- \( V_i \) is the initial volume.
Step 2: Substituting the given values.
We are given: - \( T = 27^\circ C = 27 + 273 = 300 \, \text{K} \), - \( V_i = 0.4 \, \text{L} \), - \( V_f = 0.8 \, \text{L} \). Substitute these into the equation for work: \[ W = nR(300) \ln \frac{0.8}{0.4} = nR(300) \ln 2 \] Step 3: Conclusion.
Thus, the isothermal work done is \( W = nR(300) \ln 2 \). To calculate the exact value, we need the number of moles \( n \) and the value of the gas constant \( R \).