Question

For Diatomic gas, find the ratio of \(\Delta Q : \Delta U : W\) for an isobaric process.

Hint:

In an isobaric process, the heat added to the system is split between changing the internal energy and doing work. For diatomic gases, the ratio of these quantities can be derived from the heat capacities at constant volume and pressure.

Answer 1

Correct Answer: 2

Step 1: First Law for Isobaric Process. For a process at constant pressure (isobaric), the heat supplied \(\Delta Q\) is related to the internal energy change \(\Delta U\) and work done \(W\) by the equation \(\Delta Q = \Delta U + W\).

Step 2: Defining the Molar Heat Capacities. For a diatomic gas:  
1. Molar heat capacity at constant volume \(C_v = \frac{5}{2}R\). 2. Molar heat capacity at constant pressure \(C_p = C_v + R = \frac{7}{2}R\).

Step 3: Expressing Thermodynamic Quantities. 1. \(\Delta Q = n C_p \Delta T = n(\frac{7}{2}R)\Delta T\). 2. \(\Delta U = n C_v \Delta T = n(\frac{5}{2}R)\Delta T\). 3. \(W = P \Delta V = n R \Delta T\).

Step 4: Calculating the Ratio. The ratio \(\Delta Q : \Delta U : W\) is:

\[\frac{7}{2}nR\Delta T : \frac{5}{2}nR\Delta T : nR\Delta T\]

Dividing by \(nR\Delta T\) and multiplying by 2, we get 7 : 5 : 2.