Question

Consider a system containing one mole of a diatomic gas, contained in a piston. What is the temperature change of the gas, if $q=100J$ and $W=-200J?$
(Given $C_v=\frac{5}{2}R,R=8.3J{K}^{-1}mo{l}^{-1}$ )

• A. $-2.41K$
• B. $-4.82K$
• C. $-3.62K$
• D. $-1.50K$

Answer 1

The correct option is B $-4.82K$

According to the first law of thermodynamics,
$△U=q+W=100-200=-100J$

Molar heat capacity at constant volume is given as:
$C_{v,m}={\left(\frac{△U}{n△T}\right)}_v\therefore △T=\frac{△U}{C_{v,m}}=\frac{-100J}{\frac{5}{2}R}=\frac{-100}{\frac{5}{2}\times 8.3}K$
$=-4.82K$