# Chemical Thermodynamics Chapter 4 Chemistry Class 12 Textbook Solution

### 1. Select the most apropriate option.

ii. A gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 bar from an initial volume of 2.5 L to a final volume of 4.5 L. The change in internal energy, ΔU of the gas will be

a. -500 J

b. + 500 J

c. -1013 J

d. + 1013 J

-500 J

Explanation:-Since the container is well-insulated, this process can be considered adiabatic, meaning there is no heat exchange with the surroundings. In an adiabatic process, we can use the following equations:

Change in internal energy (\(\Delta U\)) is equal to the work done (\(W\)), which is given by:

\[ \Delta U = - P_{\text{ext}} \Delta V = - P_{\text{ext}} (V_2 - V_1) \]Where:

Initial volume (\(V_1\)) = 2.5 L = 2.5 dm\(^3\)

Final volume (\(V_2\)) = 4.5 L = 4.5 dm\(^3\)

External pressure (\(P_{\text{ext}}\)) = 2.5 bar

Now, we can calculate the change in internal energy (\(\Delta U\)):

\[ \Delta U = - 2.5 \, \text{bar} \times (4.5 \, \text{dm}^3 - 2.5 \, \text{dm}^3) \]Using the conversion factor \(1 \, \text{dm}^3 \, \text{bar} = 100 \, \text{J}\), we can express this in joules:

\[ \Delta U = - 5.0 \, \text{dm}^3 \, \text{bar} \times \frac{100 \, \text{J}}{1 \, \text{dm}^3 \, \text{bar}} \]So, the change in internal energy (\(\Delta U\)) is:

\[ \Delta U = - 500 \, \text{J} \]Chemical Thermodynamics Chapter 4 Chemistry Class 12 Textbook Solution