Change in internal energy calculation

Question

What is the change in internal energy, ΔE, when 1.57 moles of a diatomic ideal gas is heated from 89°C to 306°C? How would the value be different if the ideal gas was monatomic?

Answer 1

Delta E = n x C x delta T, where n = number of moles, C is the heat capacity, and delta T is the temperature change.

For ideal gases, diatomics have C = 5R/2, and monatomics have C = 3R/2. This is C_v, where the volume is constant. When pressure is constant, and volume changes, calculate C_p by adding R to each of these values to get 7R/2 and 5R/2, respectively.

n = 1.57 and delta T = 306 - 89 = 217.

Use R = 8.314 J/mol-K and plug in to the Delta E equation above. For large values, as here, you may express the answers in kJ (kilojoules), in which case divide by 1000.