Question

One mole of an ideal gas is subjected to a process in which $P$ (in atm) $=\frac{1}{8.21}$ $V$(in litre). If the process is operating from an initial pressure 1 atm to final pressure 10 atm (no higher pressure achieved during the process) then what would be the maximum temperature obtained?

• A. $T_4=6000K$
• B. $T_4=7000K$
• C. $T_4=10000K$
• D. $T_4=8000K$

Answer 1

Answer: (C)

$T_4=10000K$

For 1 mole of an ideal gas $PV=RT$

Substitute $V=8.21P$ in the above equation.

$\frac{8.21P^2}{R}=T$

$T=\frac{8.21P^2}{0.0821}=100P^2$

Thus, the temperature will be maximum when $P^2$ is maximum or P is maximum.

Thus, maximum temperature is $100\times {10}^2=10000K$

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