The $\Delta U^{\theta}$ of combustion of methane is $-X \ kJ \ mol^{-1}.$ The value of $\Delta H^{\theta}$ is

$A$ gas is allowed to expand in a well-insulated container against a constant external pressure of $2.5 \ atm$ from an initial volume of $2.50 \ L$ to a final volume of $4.50 \ L$. The change in internal energy $\Delta U$ of the gas in joules will be .............. $J$.

Identify the reaction for which $\Delta H \neq \Delta E$ :

For the reaction $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l)$ at constant temperature,the value of $\Delta H - \Delta U$ is:

Given below are two statements.
Statement-$I$ : Adiabatic work done is positive when work is done on the system and internal energy of the system increases.
Statement-$II$ : No work is done during free expansion of an ideal gas.
In the light of the above statements,choose the correct answer from the options given below.

When $x \ kJ$ heat is provided to a system,work equivalent to $y \ J$ is done on it. What is the internal energy change during this operation?