To find the change in the internal energy of air when it is heated at constant volume, we use the formula for heat transfer at constant volume, which is given by:

$$\Delta U = m c_v \Delta T$$

Where:

• $$\Delta U$$ is the change in internal energy,
• $$m$$ is the mass of the substance (in this case, air),
• $$c_v$$ is the specific heat at constant volume,
• $$\Delta T$$ is the change in temperature.

Given that:

• The mass of air, $$m = 0.08 \, \text{kg},$$
• The specific heat of air at constant volume, $$c_v = 0.17 \, \text{kcal/kg}^{\circ}\text{C},$$
• The change in temperature, $$\Delta T = 5^{\circ} \text{C},$$
• And the conversion factor from calories to Joules, $$1 \, \text{cal} = 4.18 \, \text{J}.$$

First, convert the specific heat from kcal to Joules:

$$c_v = 0.17 \, \text{kcal/kg}^{\circ}\text{C} \times 1000 \, \text{cal/kcal} \times 4.18 \, \text{J/cal} = 710.6 \, \text{J/kg}^{\circ}\text{C}$$

Now, substitute the values into the formula:

$$\Delta U = 0.08 \times 710.6 \times 5$$

$$\Delta U = 284 \, \text{J}$$

Thus, the change in internal energy is approximately 284 Joules.