Question

A rigid and insulated tank of $3m^3$ volume is divided into two compartments. One compartment of volume of $2m^3$ contains an ideal gas at $0.8314MPa$ and $400K$ and while the second compartment of volume $1m^3$ contains the same gas at $8.314MPa$ and $500K$. If the partition between the two compartments is ruptured, the final temperature of the gas is:

• A. $420K$
• B. $450K$
• C. $480K$
• D. None of these

Answer 1

The correct option is C $480K$

The amount of heat lost by the gas in second compartment will be equal to the amount of heat gained by the gas in first compartment.
$mC\Delta T=m^{\prime }C\Delta T^{\prime }$
But $m=nM=\frac{PVM}{RT}$
Hence, $\frac{PV}{T}\Delta T=\frac{P^{\prime }{V}^{\prime }}{T^{\prime }}\Delta T^{\prime }$
Substitute values in the above expression.
$\frac{0.8314\times 2}{400}\times (T-400)=\frac{8314\times 1}{500}(500-T)$
Hence, $T=480K$