Two kilograms of air is heated at constant pressure of 200 kPa to 500^∘ C. Calculate the entropy

step 1 Hello students, in this problem we have air having mass 2 kg is heated at constant pressure from

Two kilograms of air is heated at constant pressure of 200...

Two kilograms of air is heated at constant pressure of $200 \mathrm{kPa}$ to $500^{\circ} \mathrm{C}$. Calculate the entropy change if the initial volume is $0.8 \mathrm{~m}^{3}$. The initial temperature is found to be $$ T_{1}=\frac{P_{1} V_{1}}{m R}=\frac{(200)(0.8)}{(2)(0.287)}=278.7 \mathrm{~K} $$ The entropy change is then found, using (6.16) to be $$ \Delta S=m\left[C_{p} \ln \frac{T_{2}}{T_{1}}-R \ln 1\right]=(2)(1.00) \ln \frac{773}{278.7}=2.040 \mathrm{~kJ} / \mathrm{K} $$

Two kilograms of air is heated at constant pressure of $200 \mathrm{kPa}$ to $500^{\circ} \mathrm{C}$. Calculate the entropy change if the initial volume is $0.8 \mathrm{~m}^{3}$.
The initial temperature is found to be
$$
T_{1}=\frac{P_{1} V_{1}}{m R}=\frac{(200)(0.8)}{(2)(0.287)}=278.7 \mathrm{~K}
$$
The entropy change is then found, using (6.16) to be
$$
\Delta S=m\left[C_{p} \ln \frac{T_{2}}{T_{1}}-R \ln 1\right]=(2)(1.00) \ln \frac{773}{278.7}=2.040 \mathrm{~kJ} / \mathrm{K}
$$

Key Concepts

Specific Heat Capacity (at Constant Pressure)

Specific heat capacity at constant pressure, denoted as C_p, is the amount of heat required to raise the temperature of a unit mass of a substance by one degree at constant pressure. This property is crucial in thermodynamics when analyzing processes that occur at constant pressure, as it helps quantify the heat interaction and corresponding change in entropy.

Constant Pressure Process

In a constant pressure process, the pressure remains fixed while other state variables such as volume and temperature may change. This condition allows the use of specific heat at constant pressure (C_p) to calculate the heat absorbed or released during the process, and it simplifies the entropy change formula by eliminating terms related to pressure variations.

Entropy Change

Entropy is a measure of the disorder or randomness in a system and is a state function in thermodynamics. The change in entropy for a process, especially for an ideal gas, is determined by integrating the reversible heat transfer over temperature. For processes with variable temperature, this often involves logarithmic functions to account for the natural change in entropy as the system heats or cools.

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and amount of a gas using the equation PV = mRT. This law is fundamental in calculating any unknown state variable when the other variables are known, allowing one to determine the properties of the gas under specific conditions, which is essential for analyzing processes in thermodynamics.

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