$A$ mixture of gas expands from $0.03\, m^3$ to $0.06\, m^3$ at a constant pressure of $1\, MPa$ and absorbs $84\, kJ$ of heat during the process. The change in internal energy of the mixture is $.....\, kJ$.

Assuming that water vapour is an ideal gas,the internal energy change $(\Delta U)$ when $1\, mol$ of water is vaporised at $1\, bar$ pressure and $100\, ^{\circ}C$,(given: molar enthalpy of vaporisation of water at $1\, bar$ and $373\, K = 41\, kJ\, mol^{-1}$ and $R = 8.3\, J\, mol^{-1}\, K^{-1}$) will be .............. $kJ\, mol^{-1}$

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

If $5 \ kJ$ of work is done on the system and $1 \ kJ$ of heat is released by the system,find the change in internal energy in $kJ$.

$5 \, mol$ of an ideal gas expands isothermally and irreversibly from a pressure of $10 \, atm$ to $1 \, atm$ against a constant external pressure of $1 \, atm$. The work done $(w_{irr})$ at $300 \, K$ is:

If $1 \ L$ of an ideal gas at a pressure of $20 \ atm$ expands isothermally and reversibly to a final volume of '$X$' $L$ by absorbing $92.12 \ L \ atm$ heat,'$X$' (in $L$) is