# VT graph thermodynamics

If we have one mole monoatomic ideal gas was taken through process AB as shown in the figure then ∆ S is positive and work is also positive but how can we find the value of work and heat absorbed as pressure is changing .k

• From what you learned in middle school algebra, what is the equation for the straight line between points A and B in terms of V and T? If you solve this equation for T and substitute it into the ideal gas law, what do you get for P in terms of V? What is the equation for the work in terms of P and V? If you know the work and the change in internal energy, do you know the heat? – Chet Miller Dec 18 '15 at 12:53
• Yes but I forget that – user101522 Dec 18 '15 at 12:56
• Do you remember it now, or do you need to go back to your old algebra text book? This is not really a chemistry question, it's a math question. – Chet Miller Dec 18 '15 at 13:00
• But can you help me – user101522 Dec 18 '15 at 13:03
• Can you help yourself? He literally spelt out everything you need to do. Start by finding $p$ in terms of $V$. Google "equation of a straight line through two points" if you need maths help. – orthocresol Dec 18 '15 at 13:04

Since you know the number of moles of ideal gas, you can find the inital and final pressures with the ideal gas law: $PV = nRT$. For entropy you may first take that $U = \frac{3}{2} nRT$, and that $dU = \delta Q + \delta W$.  $\delta Q$ and $\delta W$ may be substituted by $\delta Q = T \mathrm{d}S$, and $\delta W = -p\mathrm{d}V$. This should be enough for you to solvew the problem.
• You find d$S$ because you know everything else. – A.K. Dec 18 '15 at 15:44