An ideal gas absorbs $210 \ J$ of heat and undergoes expansion from $3 \ L$ to $6 \ L$ against a constant external pressure of $10^5 \ Pa$. What is the value of $\Delta U$ (in $J$)?

Which of the following is the correct mathematical expression for the first law of thermodynamics?

For $1 \, \text{mol}$ of an ideal gas,isothermal expansion occurs from $1 \, \text{L}$ to $10 \, \text{L}$ in a vacuum at $300 \, \text{K}$. What is the value of $\Delta U$ for this process? $(R = 2 \, \text{cal} \, \text{K}^{-1} \, \text{mol}^{-1})$

An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process?

If $\Delta E$ is the heat of reaction for $C_2H_5OH_{(l)} + 3O_{2(g)} \longrightarrow 2CO_{2(g)} + 3H_2O_{(l)}$ at constant volume,the $\Delta H$ (heat of reaction at constant pressure) at constant temperature is

For the reaction $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$ at $977 \, ^\circ C$,$\Delta H = 174 \, kJ/mol$. Calculate $\Delta U$ in $kJ$.