Question

One Ilitre of a gas weighs $2g$ at $300K$ and $1$ atm pressure. If the pressure is made $0.75$ atm at which of the following temperatures will one litre of the same gas, weigh one gram?

• A. $450K$
• B. $600K$
• C. $800K$
• D. $900K$

Answer 1

The correct option is A $450K$

Assembling all the data we get,

$P_1=1atm;W_1=2g$

$P_2=0.75atm;W_2=1g$

$T_1=300K;V_1=1L$

$T_2=?;V_2=1L$

So we know that,

$\frac{P_1{V}_1}{P_1{V}_1}=\frac{W_1{T}_1}{W_2{T}_2}$

Substituting in the above formula we get,

=> $\frac{1\times 1}{0.75\times 1}=\frac{2\times 300}{1\times T_2}$

=> $\frac{1}{0.75}=\frac{600}{T_2}$

Cross Multiplying we get,

=> $T_2\times 1=600\times 0.75$

=> $T_2=450K$

Therefore the required temperature is $450K$.