Question
A pressure cooker contains 2 moles of an ideal diatomic gas at . The gas is heated isobarically (constant pressure) until its volume doubles. Find the work done by the gas, the heat absorbed, and the change in internal energy. Take .
Solution — Step by Step
For an isobaric process on an ideal gas, . Volume doubles, so temperature also doubles:
So .
For isobaric processes, :
Positive, because the gas expands and pushes the piston outward.
For a diatomic ideal gas, . Internal energy depends only on temperature:
Or equivalently with , giving J. Cross-check passes.
Final: J, J, J.
Why This Works
Notice how heat splits cleanly: about 71% goes into raising internal energy (heating the gas) and 29% goes into pushing the piston. That ratio depends on , which depends on the gas type — diatomic, monatomic, or polyatomic.
The pressure cooker analogy works because once the regulator opens, the process is approximately isobaric at the design pressure. Steam takes in heat partly to vaporise more water (latent heat, ignored here) and partly to push the regulator weight up (work).
Alternative Method
Using for diatomic gas:
Same answer, fewer calculations if you remember .
Common Mistake
Students use to compute heat in an isobaric process. Wrong — at constant pressure, you must use . The relation only applies when volume is constant.