$500 \ J$ of energy is transferred as heat to $0.5 \ mol$ of Argon gas at $298 \ K$ and $1.00 \ atm$. The final temperature and the change in internal energy respectively are $:$ Given $: R = 8.3 \ J \ K^{-1} \ mol^{-1}$

Calculate $\Delta H^{\circ}$ for the reaction,$Na_2O_{(s)} + SO_{3(g)} \longrightarrow Na_2SO_{4(s)}$,given the following reactions:
$(A) \ Na_{(s)} + H_2O_{(l)} \longrightarrow NaOH_{(s)} + \frac{1}{2}H_{2(g)} \quad \Delta H^{\circ} = -146 \ kJ$
$(B) \ Na_2SO_{4(s)} + H_2O_{(l)} \longrightarrow 2NaOH_{(s)} + SO_{3(g)} \quad \Delta H^{\circ} = +418 \ kJ$
$(C) \ 2Na_2O_{(s)} + 2H_{2(g)} \longrightarrow 4Na_{(s)} + 2H_2O_{(l)} \quad \Delta H^{\circ} = +259 \ kJ$

Which of the following relations is correct?

Calculate $\Delta H_f^o$ of $SiH_2$ from the following reactions:
$Si_2H_{6(g)} + H_{2(g)} \to 2SiH_{4(g)}, \Delta H = -11.7 \ kJ/mol$
$SiH_{4(g)} \to SiH_{2(g)} + H_{2(g)}, \Delta H = +239.7 \ kJ/mol$
$\Delta H_f^o(Si_2H_{6(g)}) = 80.3 \ kJ/mol$

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?

$A$ thermodynamic cycle in the pressure $(p)-$ volume $(V)$ plane is given below. $A B$ and $C D$ are isothermal processes while $B C$ and $D A$ are adiabatic processes. The same cycle in the temperature $(T) -$ entropy $(S)$ plane is