A mole of nitrogen is heated under isobaric conditions from 20 degree Celsius to 50 degree Celsius. How much heat is required to do this?

For this problem, nitrogen can be taken to be a
calorically perfect gas. When the temperature of the gas is increased under isobaric
conditions, work has to be done on the gas which contributes to an increase in its
internal energy and an increase in its volume.

The total
work done is given by the relation W = n*Cp*dT where n is the number of moles of the
gas, Cp is specific heat at a constant pressure and dT is the change in temperature. For
diatomic gases Cp = (7/2)*R where R is the universal gas constant 8.314
J/(K*mol).

Heating the gas from 20 degree Celsius to 50
degree Celsius is equivalent to an increase in temperature of 30 degree Celsius or 30
Kelvin. This requires an addition of heat equal to

W =
(7/2)*8.314*30 = 872.97 J

The heating of
nitrogen from 20 degree Celsius to 50 degree Celsius under isobaric conditions requires
an addition of heat equal to 872.97 J.