Question

By heating 2 mol of nitrogen gas in a frictionless piston-cylinder, the gas expands at a constant pres- sure of 1 bar from an initial volume of 0.02 m² to a final volume of 0.05 m. The gas temperature correspondingly increases from 300 to 500 K. Assuming nitrogen is an ideal gas with a molar heat capacity CP = R (where R is the gas constant), find the amount of heat added and work derived from the gas expansion.

Answer 1

Step-by-step explanation:

The given data is as follows.

n = 2,
`V_(1) = 0.02 m^(2)`,
`V_(2) = 0.05 m^(2)`

`T_(1) = 0.02 m^(2)` = 300 K ,
`T_(2)` = 500 K

P = 1 bar

Equation for work done will be as follows.

W =
`-P * \Delta V`

=
`-1 bar * (0.05 m^(2) - 0.02 m^(2))`

= - 3000 J

Hence, formula for heat added is as follows.

Q =
`nC_(p) \Delta T`

Putting given values into the above formula as follows.

Q =
`nC_(p) \Delta T`

=
`2 * (7)/(2) * (500 K - 300 K)`

= 11639.6 J

Thus, we can conclude that the amount of heat added is 11639.6 J.