When two mole of an ideal gas (Cp, m=(5)/(2) R) heated from 300 K to 600 K at constant pressur

step 1 Hello students in this question we have number of moles equals to two of an ideal gas which is h

When two mole of an ideal gas (Cp, m=(5)/(2) R) heated from...

When two mole of an ideal gas $\left(C_{p, m}=\frac{5}{2} R\right)$ heated from $300 \mathrm{~K}$ to $600 \mathrm{~K}$ at constant pressure. The change in entropy of gas $(\Delta S)$ is : $\begin{array}{llll}\text { (b) }-\frac{3}{2} R \ln 2 & \text { (c) } 5 R \ln 2 & \text { (d) } \frac{5}{2} R \ln 2\end{array}$ (a) $\frac{3}{2} R \ln 2$

When two mole of an ideal gas $\left(C_{p, m}=\frac{5}{2} R\right)$ heated from $300 \mathrm{~K}$ to $600 \mathrm{~K}$ at constant pressure.
The change in entropy of gas $(\Delta S)$ is :
$\begin{array}{llll}\text { (b) }-\frac{3}{2} R \ln 2 & \text { (c) } 5 R \ln 2 & \text { (d) } \frac{5}{2} R \ln 2\end{array}$
(a) $\frac{3}{2} R \ln 2$

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, the change in entropy during a process can be calculated by integrating the reversible heat transfer divided by the temperature (dS = dQ/T). For processes carried out at constant pressure, this leads to the expression ?S = nC_p ln(T2/T1), linking entropy change to temperature change.

Isobaric Process

An isobaric process is one that occurs at constant pressure. In such a process, the heat transferred to or from the system is directly related to the change in temperature. The constant pressure condition simplifies many thermodynamic calculations, including the determination of entropy change, since the molar heat capacity at constant pressure, C_p, remains applicable throughout.

Molar Heat Capacity at Constant Pressure (C_p)

The molar heat capacity at constant pressure, C_p, is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius while keeping the pressure constant. This property is fundamental in thermodynamics for calculating the heat transferred and corresponding changes in state variables like entropy during processes occurring at constant pressure.

Ideal Gas

An ideal gas is a theoretical construct that follows the ideal gas law (PV = nRT), where interactions between molecules are neglected except for elastic collisions. This simplification allows for the direct application of thermodynamic relations, such as the calculation of entropy change using constant molar heat capacities, making it easier to analyze processes like isobaric heating or cooling.

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