Question

To practice Problem-Solving Strategy 19.1 The First Law of Thermodynamics. A 3.00 mol sample of carbon dioxide undergoes a two-step process. First, at a constant volume, the gas behaves ideally as it is cooled from 39.0 ?C to -78.5 ?C where it reaches a pressure of 1 atm. Second, at -78.5 ?C and a constant pressure of 1 atm the gas undergoes a phase change to dry ice. What is the change in internal energy of carbon dioxide for this entire process? The constant volume molar heat capacity of carbon dioxide gas CV is 28.46 J/mol?K, the heat of sublimation Ls of carbon dioxide is 6030 cal/mol, and the density of dry ice ?dryice is 3.41×104 mol/m3. What is the change in internal energy ?U of carbon dioxide for this entire process?

Answer 1

From first law of thermodynamics, we have

where Q is heat , p is pressure and V is volume. As the gas cooled with constant volume so dV is zero. All change in internal energy is due to heat.

where n is number of moles C_v is the constant volume molar heat capacity and delta T is change of temperature. So we have

Now when gac will condense to ice it will loose heat which will be equal to the change in internal energy.

So total change in internal energy is sum of both which is -21536.7103 calories. -ve sign means internal energy is decreasing.