For water at $100^{\circ} C$ and $1 \, bar$,$\Delta_{vap} H - \Delta_{vap} U = ...... \times 10^{2} \, J \, mol^{-1}$. (Round off to the Nearest Integer) $[Use : R = 8.31 \, J \, mol^{-1} \, K^{-1}]$ [Assume volume of $H_{2}O_{(\ell)}$ is much smaller than volume of $H_{2}O_{(g)}$. Assume $H_{2}O_{(g)}$ treated as an ideal gas]

Which of the following relations is correct for the reaction $S(s) + O_2(g) \rightarrow SO_2(g)$?

Express the change in internal energy of a system when
$(i)$ No heat is absorbed by the system from the surroundings,but work $(w)$ is done on the system. What type of wall does the system have?
$(ii)$ No work is done on the system,but $q$ amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
$(iii)$ $w$ amount of work is done by the system and $q$ amount of heat is supplied to the system. What type of system would it be?

In a cylinder,$1.0 \, \text{kcal}$ of heat is added to $1.2 \, \text{L}$ of $O_2$ gas at a constant pressure of $1 \, \text{atm}$. The volume changes to $1.5 \, \text{L}$. Calculate the change in internal energy $(\Delta U)$ for this process. (in $, \text{kcal}$)

If the internal energy of an ideal gas decreases by the same amount of the work done by the system,the process is

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