# Difference between reversible and irreversible heat transfer

Reference books define reversible heat transfer as heat transfer occurs across a infinitesimal thermal gradient i.e. dT and irreversible heat transfer as heat transfer across finite thermal gradient i.e. ΔT.

Now i want to calculate the quantity $$\int _1^2 \frac{dq}{T}$$ for a process involving heat transfer into a system where its temperature changed from $$T_{1}$$ to $$T_{2}$$. My question is if i calculate this integral for a reversible and and an irreversible heat transfer into a system whether they will be equal?

• Thank you for the answer. Now I am able to digest the second law of thermodynamics also. As per your answer $$\int _1^2 \frac{dq_{rev}}{T} = \int _1^2 \frac{dq}{T} + \sigma$$. $\sigma$ a positive integer. You had given method to find out the integral on the RHS. – Anoop A K Apr 18 at 6:32
• $\sigma$ is definitely not an integer. It is just a positive number. – Chet Miller Apr 18 at 12:07