Question

During an adiabatic compression, $830J$ of work done on $2$ moles of a diatomic ideal gas to reduce its volume by $50$%. The change in its temperature is nearly $(R=8.3J{K}^{-1}{mole}^{-1})$

• A. $14K$
• B. $33K$
• C. $40K$
• D. $20K$

Answer 1

The correct option is D $20K$

$\text{Given:-}$ $W=830J$

$Numberofmoles=2moles$

$\text{Solution:-}$

In adiabatic process

$W=-\Delta U$

Since, $\Delta U=n{C}_V\Delta T$

$\Rightarrow \Delta T=\frac{-W}{n{C}_V}=\frac{-(-830)}{2\times \left(5/2\right)\times R}$

$\Rightarrow \Delta T=\frac{830}{5\times 8.314}=20K$

$\text{Hence the correct option is D}$