One mole of an ideal monoatomic gas at temperature $T$ expands adiabatically in an insulated flask from $1 \ L$ to $2 \ L$ against an external pressure of $1 \ atm$. What is the final temperature?

Enthalpy of combustion of $CH_4, C_2H_6$ and $C_3H_8$ are $-210.8, -368.4$ and $-526.2 \ k \ cal \ mol^{-1}$ respectively. Enthalpy of combustion of hexane can be predicted as........$k \ cal \ mol^{-1}$

$A$ solution of $500 \ mL$ of $2 \ M \ KOH$ is added to $500 \ mL$ of $2 \ M \ HCl$ and the mixture is well shaken. The rise in temperature $T_1$ is noted. The experiment is then repeated using $250 \ mL$ of each solution and the rise in temperature $T_2$ is again noted. Assume all heat is absorbed by the solution.

For the reaction,$2Cl_{(g)} \to Cl_{2(g)}$,the signs of $\Delta H$ and $\Delta S$ respectively,are:

State $1 \longleftarrow$ State $2 \longleftarrow$ State $3$
$\left(\begin{array}{c} T=300 \ K \\ P=15 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=10 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=5 \ bar \\ 1 \ mole \end{array}\right)$
The above shows a cyclic process. Calculate the total work done during one complete cycle. (Assume a single step to reach the next state).

Consider the reversible processes for $1.0 \ mol$ of an ideal gas. $w_1, w_2, w_3$ and $w_4$ represent work done (in calories) in the processes $1, 2, 3$ and $4$, respectively; $\Delta U_2$ and $\Delta U_4$ are changes in the internal energy for the processes $2$ and $4$, respectively. (use $R = 2 \ cal \ K^{-1} \ mol^{-1}$). The correct option is: