Question

How much energy must be transferred as heat for a reversible isothermal expansion of an ideal gas at $\mathbf{132}\mathbf{°}\mathit{C}$if the entropy of the gas increases by 46.0 J/K?

Short answer

The amount of energy to be transferred as heat is$1.86\times {10}^{4}J$

Step-by-step solution

The given data

1. The temperature at which isothermal process takes place,$T=132°Cor450K$
2. The entropy change of the gas,$∆S=46.0J/K$

Understanding the concept of entropy change

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. We can write the expression for energy transferred as heat by rearranging the formula for change in entropy for a reversible isothermal process. After inserting the given values, we can get the energy that must be transferred as heat for a reversible isothermal expansion of an ideal gas.

Formula:

The entropy change of the gas, $∆S=\frac{Q}{T}$ …(i)

Calculation of the heat transferred by the gas

Using the equation (i) and the given data, the amount of heat transferred by the body can be given as:

$\begin{array}{l}Q=T∆S\\ =405K\times 46J/K\\ =18630J\\ \approx 1.86\times {10}^{4}J\end{array}$

Hence, the value of the energy transferred as heat by the gas is$1.86\times {10}^{4}J$