Chapter 20: Q58P (page 607)

Repeat Problem 57, with the pressure now kept constant.

Short Answer

Expert verified

The change in the entropy of the gas at constant pressure is 5.98 J/K

Step by step solution

The given data

The number of moles is n = 1.00 mol .

The gas ismonatomic.

The initial temperature is $T_{i} = 300 K$ .

The final temperature is $T_{f} = 400 K$ .

The pressure is constant.

Understanding the concept of entropy change

By finding the equation for heat absorbed at constant pressure and using Equation 20-1, we can find the change in the entropy of the gas at constant pressure.

Formula:

The energy absorbed as heat by the gas at constant pressure, $dQ = \frac{5}{2} nRdT$ (1)

The change in entropy of the gas, $∆ S = \int \frac{dQ}{T}$ (2)

Calculation of the entropy change

Since the pressureis kept constant, substituting the value of equation (1) in equation (2), we can get the change in entropy as given:

$∆ S = \int_{T_{i}}^{T_{f}} \frac{(\frac{5 nR}{2}) dT}{T} = \frac{5}{2} nRln (\frac{T_{f}}{T_{i}}) = \frac{5}{2} \times 1.00 mol \times 8.31 \frac{J}{mol \cdot K} \times (\frac{400 K}{300 K}) = 5.98 J / K$