0
$\begingroup$

The heat capacity of one mole of an ideal gas is found to be $C_{v}=3R(1+aRT)/2$ where $a$ is a constant. The book provides the solution to this problem but there is a step in which $(1+aRT)=e^{aRt}$ How is this possible? Please explain.

$\endgroup$
  • $\begingroup$ I'm guessing you are given $nC_vdT=n\frac{3}{2}R(1+aRT)dT=-PdV=-\frac{nRT}{V}dV$. Correct? $\endgroup$ – Chet Miller Oct 29 '19 at 17:51
  • $\begingroup$ ${}$ Which book? $\endgroup$ – Qmechanic Oct 29 '19 at 19:34
  • 1
    $\begingroup$ The equation you are asking about is an approximation. If you expand $e^{aRT}$ in a Taylor series about aRT=0, the first two terms are 1 + aRT. $\endgroup$ – Chet Miller Oct 30 '19 at 1:24
2
$\begingroup$

If $aRT$ is extremely small then $$e^{aRT} \approx 1+aRT$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.