Question

An open vessel containing air at 27${}^o$C is heated to 127${}^o$C. The fraction of air originally present in the bottle that is expelled is:

• A. 50%
• B. 25%
• C. 33%
• D. 40%

Answer 1

The correct option is C 33%

Initial temperature $T=27{}^{o}C=27+273K=300K$.

Final temperature $T^{\prime }=127{}^{o}C=127+273K=400K$.

Initial volume $=V$

Final volume $=V^{\prime }$

$\frac{V^{\prime }}{V}=\frac{T^{\prime }}{T}=\frac{400}{300}=1.33$

The fraction of air originally present in the bottle that is expelled is

$\frac{V^{\prime }-V}{V}=\frac{1.33-1}{1}=0.33=33$ %

Hence, the correct option is $\text{C}$