Isothermal Process

The Isothermal Process is the process in which the temperature remains constant in the system. Some heat transfer does take place but it is typically at an extremely slow rate which enables it to attain thermal equilibrium. 

Since, W = ∫PdV

From Gas Law, 

PV = nRT

P = nRT/V 

Putting the value of P, we get:

W = nRT VB∫VAdVV 

W = nRT ln VBVA

If VB > VA, the work done will be positive.

If VB < VA, the work done is negative.

Internal energy is constant in such systems because the temperature is constant, ΔU = 0. Therefore, according to the first law of thermodynamics, 

Q = ΔU + W 

Therefore, Q = W.