Question

Consider a system containing one mole of a diatomic gas, contained by a piston. What is the temperature change of the gas, if $q=50J$ and $W=-100J?$
(Given $C_v=\frac{5}{2}R$ )

• A. $-50K$
• B. $-2.4K$
• C. $-5.8K$
• D. $-1.25K$

Answer 1

The correct option is B $-2.4K$

According to the first law of thermodynamics,
$△U=q+W=50-100=-50J$

Molar heat capacity at constant volume is given as:
$C_{v,m}={\left(\frac{△U}{n△T}\right)}_v\therefore △T=\frac{△U}{C_{v,m}}=\frac{-50J}{\frac{5}{2}R}=\frac{-50}{\frac{5}{2}\times 8.314}=-2.41K$