Question

A piston filled with $0.04$ moles of an ideal gas expands reversibly from $50.0\text{mL}\text{to}375\text{mL}$ at a constant temperature of $37.0{}^o\text{C}$. As it does so, it absorbs $208\text{J}$ of heat. What will be the value of $q$ and $W$ respectively ?

• A. $+208,+208$
• B. $-208,-208$
• C. $+208,-208$
• D. $-208,+208$

Answer 1

The correct option is C $+208,-208$

$\text{Number of moles}=0.04\text{mol}$
$\text{Initial volume}=50.0\text{mL}$
$\text{Final volume}=375\text{mL}$
$\text{Temperature}=\text{Constant}\left(37.0{}^o\text{C}\right)$
$\text{Heat absorbed}=+208\text{J}$

We know that inernal energy is a function of temperature and here, the temperature is constant.
Hence, there is no change in the internal energy.
$dU=0$
The first law of thermodynamics is given as ;
$\Delta U=q+W$
$0=208\text{J}+W$
$W=-208\text{J}$