If you were an engineer in a power plant you might need to study the effects of heating on the air in a turbine. For some purposes, you can use nitrogen gas to model air. A sample of nitrogen gas of volume 20.0 L at 5.00 kPa is heated from 20. °C to 400.°C at constant volume. What is the change in the entropy of the nitrogen? The molar heat capacity of nitrogen at constant volume, C_V,m, is 20.81 J · K^–1?mol^–1.

ANTICIPATE Because the thermal disorder in a system increases as the temperature rises, you should expect a positive entropy change.

PLAN To use Eq. 4, first convert the temperature into kelvins and find the amount (in moles) of gas molecules by using the ideal gas law in the form n = PV/RT. Because the data are liters and kilopascals, use R expressed in those units. Then use Eq. 4, with the heat capacity at constant volume, C_V = nC_V,m. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage.

What should you assume? Assume that nitrogen is an ideal gas (for the calculation of n) and that C_V is constant over the temperature range.

Transcribed Image Text:

T₂ Cln Ti AS C ln- =