$A$ solution of $500 \ mL$ of $0.2 \ M \ KOH$ and $500 \ mL$ of $0.2 \ M \ HCl$ is mixed and stirred; the rise in temperature is $T_1$. The experiment is repeated using $250 \ mL$ each of solution,the temperature raised is $T_2$. Which of the following is true?

Products are favoured in a chemical reaction taking place at a constant temperature and pressure. Consider the following statements: $(i)$ The change in Gibbs energy for the reaction is negative. $(ii)$ The total change in Gibbs energy for the reaction and the surroundings is negative. $(iii)$ The change in entropy for the reaction is positive. $(iv)$ The total change in entropy for the reaction and the surroundings is positive. The statements which are always true are:

Consider the reaction at $300 \ K$: $H_{2(g)} + Cl_{2(g)} \to 2HCl_{(g)}$; $\Delta H^o = -185 \ kJ$. If $2 \ mole$ of $H_2$ completely react with $2 \ mole$ of $Cl_2$ to form $HCl$,what is $\Delta U^o$ for this reaction in $kJ$?

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at $1 \ bar$ pressure is given. $S_T$ and $S_0$ are entropies of the phases at temperatures $T$ and $0 \ K$,respectively.
The transition temperature for $\alpha$ to $\beta$ phase change is $600 \ K$ and $C_{p, \beta} - C_{p, \alpha} = 1 \ J \ mol^{-1} \ K^{-1}$. Assume $(C_{p, \beta} - C_{p, \alpha})$ is independent of temperature in the range of $200$ to $700 \ K$. $C_{p, \alpha}$ and $C_{p, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases,respectively.
$(1)$ The value of entropy change,$S_{\beta} - S_{\alpha}$ (in $J \ mol^{-1} \ K^{-1}$),at $300 \ K$ is. . . . . . .
$(2)$ The value of enthalpy change,$H_{\beta} - H_{\alpha}$ (in $J \ mol^{-1}$),at $300 \ K$ is.
[Use : $\ln 2 = 0.69$,Given : $S_{\beta} - S_{\alpha} = 0$ at $0 \ K$]

$C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} + 400 \; kJ$
$C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)} + 100 \; kJ$
When coal of purity $60 \%$ is allowed to burn in the presence of insufficient oxygen,$60 \%$ of carbon is converted into $CO$ and the remaining is converted into $CO_2$.
The heat generated when $0.6 \; kg$ of coal is burnt is (in $; kJ$)

$A$ system consisting of $1 \, mole$ of an ideal gas undergoes a reversible process,$A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow A$ (schematically indicated in the figure below). If the temperature at the starting point $A$ is $300 \, K$ and the work done in the process $B \rightarrow C$ is $1 \, L \, atm$,the heat exchanged in the entire process in $L \, atm$ is $....$