An ideal gas expands against a constant external pressure of $2 \ bar$ from $5 \ L$ to $8 \ L$ and absorbs $10 \ kJ$ of heat. What is $\Delta U$ of the system (in $J$)?

During the free expansion of an ideal gas in an isolated chamber,

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

$A$ gas absorbs $100 \ J$ of heat and is simultaneously compressed by a constant external pressure of $1.5 \ atm$ from a volume of $8.0 \ L$ to $2.0 \ L$. The change in internal energy for the gas in Joules is $(1 \ L \cdot atm = 101.32 \ J)$.

When $1 \, \text{mol}$ of a gas is heated at constant volume,the temperature increases from $298 \, K$ to $308 \, K$. If the heat supplied to the gas is $500 \, J$,which of the following statements is correct?

Calculate the change in internal energy of the system if $20 \ kJ$ of work is done on the system and it releases $10 \ kJ$ of heat in a particular reaction. (in $kJ$)