One mole of an ideal gas expands isothermally and reversibly from $10 \ dm^3$ to $20 \ dm^3$ at $300 \ K$. $\Delta U$,$q$ and work done in the process respectively are $:$ Given $: R=8.3 \ J \ K^{-1} \ mol^{-1}$,$\ln 10=2.3$,$\log 2=0.30$,$\log 3=0.48$

Internal energy of an ideal gas increases in:

Which of the following equations represents the first law of thermodynamics under isobaric conditions?

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $2.5 \ atm$ from $2.5 \ L$ to $4.5 \ L$. The change in internal energy of the gas in joules is: (in $J$)

Consider the reaction: $N_2(g) + 3H_2(g) \to 2NH_3(g)$ carried out at constant temperature and pressure. If $\Delta H$ and $\Delta U$ are the enthalpy and internal energy changes for the reaction,which of the following expressions is true?

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these processes are:
$Q_1 = 6000 \, J, Q_2 = -5500 \, J, Q_3 = -3000 \, J, Q_4 = 3500 \, J$
$W_1 = 2500 \, J, W_2 = -1000 \, J, W_3 = -1200 \, J, W_4 = x \, J$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $|x|$ and $\eta$ respectively are: