For the complete combustion of ethene,$C_2H_{4(g)} + 3O_{2(g)} \rightarrow 2CO_{2(g)} + 2H_2O_{(l)}$,the amount of heat produced as measured in a bomb calorimeter is $1406 \ kJ \ mol^{-1}$ at $300 \ K$. The minimum value of $T \Delta S$ needed to reach equilibrium is $(-)....... \ kJ$. (Nearest integer) Given: $R = 8.3 \ J \ K^{-1} \ mol^{-1}$

At $27 \, ^oC$,one mole of an ideal gas is compressed isothermally and reversibly from a pressure of $2 \ atm$ to $10 \ atm$. The values of $\Delta E$ and $q$ are $(R = 2 \ cal \ K^{-1} \ mol^{-1})$:

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_i$ is the initial temperature and $T_f$ is the final temperature,which of the following statements is correct?

In an adiabatic process,the work involved during expansion or compression of an ideal gas is given by

For the reaction,$2 CO + O_2 \longrightarrow 2 CO_2$; $\Delta H = -560 \ kJ$. Two moles of $CO$ and one mole of $O_2$ are taken in a container of volume $1 \ L$. They completely form two moles of $CO_2$. The gases deviate appreciably from ideal behavior. If the pressure in the vessel changes from $70 \ atm$ to $40 \ atm$,find the magnitude (absolute value) of $\Delta U$ at $500 \ K$. $(1 \ L \ atm = 0.1 \ kJ)$

One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27\,^oC$. If the work done during the process is $3\,kJ$,the final temperature will be equal to $(C_v = 20\,J\,K^{-1} \, mol^{-1})$