Question

An ideal gas $(C_v=\frac{3}{2}R)$ is maintained in a vessel of volume $83\times {10}^{-4}{m}^3$ at pressure $1.6\times {10}^{6}N{m}^{-2}$ and temperature $300K$. If $2.49\times {10}^{4}J$ heat is given to this vessel, then its final temperature will be

• A. $600K$
• B. $625K$
• C. $650K$
• D. $675K$

Answer 1

The correct option is D $675K$

$Q=n{C}_{v}dT⟹2.49\times {10}^4=\frac{PV}{RT}\times \left(C_v\right)\times (T_2-T_1)$

$2.49\times {10}^4=\frac{83\times {10}^{-4}\times 1.6\times {10}^6}{8.314\times 300}\times (1.5\times 8.314)(T_2-300)$

$T_2-300=375⟹T_2=675K$