Question

When state of a system is changed from $A$ to $B$ adiabatically the work done on the system is $322J$. Then state of the same system is changed from $A$ and $B$ by other method, $100cal$. of heat is required then work done on the system in this process will be

• A. $98J$
• B. $38.2J$
• C. $15.9J$
• D. $16.9J$

Answer 1

The correct option is A $98J$

Given,

$W_{AB\left(adiabatic\right)}=-322J$ (work done on the system)

$Q_{AB\left(other\right)}=+100cal=100\times 4.2JCa{l}^{-1}=+420J$

Let suppose change in internal energy is $\Delta U_{AB}$

Now,

$Q=\Delta U+W$

$Q_{AB\left(adia\right)}=\Delta U_{AB}+(-322)=0$. (1)

$Q_{AB\left(other\right)}=\Delta U_{AB}+W_{AB\left(other\right)}=420$ (2)

Subtract equation 1 - equation 2,

$W_{AB\left(other\right)}+322=420$

$W_{AB\left(other\right)}=98\text{Joules.}$

Option $\text{A}$ is the correct answer.