Question

Calculate the final volume (in L) of one mole of an ideal gas initially at $0^o$C and $1$ atm pressure, if it absorbs $2000$ cal of heat during a reversible isothermal expansion.

Answer 1

Let us consider the problem:

AT stp; the gas is the pressure and standard temperature condition

$v^1=22.4d{m}^3\left(given\right)$

$v_2=?\left(findout\right)$

Let we know that

$\Delta U=q+w$

$\Delta U=0$ (isotherm and resistible for given expression)

$\Rightarrow$

$q=-w=2000cal$

$=2000\times 4.184=8368$

woek done $w{=}_{n}RT{/}_n\left(\frac{v_2}{v_1}\right)$

Therefore

$-w=8368J=Nrt/n\left(\frac{v_2}{v_1}\right)$

$\Rightarrow$ $\left(im01\right)\times \left(8.314J{k}^{-1}m{01}^{-1}\right)\left(273k\right)/n\left(\frac{v_2}{02.5dm}\right)$

hence,

$v_2=242.50d{m}^3$