First law and internal energy

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant $R = 8.0\ \mathrm{J\,mol^{-1}\,K^{-1}}$, the decrease in its internal energy, in Joule, is__________.

Which of the following options is the only correct representation of a process in which $\Delta U = \Delta Q - P\Delta V$?

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i=10^5$ Pa and volume $V_i=10^{-3}\ \mathrm m^3$ changes to a final state at $P_f=(1/32)\times10^5$ Pa and $V_f=8\times10^{-3}\ \mathrm m^3$ in an adiabatic quasi-static process, such that $P^3V^5=$ constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$ followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately

200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $T_1$, pressure $P_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$, pressure $P_2$ and volume $V_2$. During this process the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)

A thermodynamic system is taken from an initial state $i$ with internal energy $U_i=100$ J to the final state $f$ along two different paths $iaf$ and $ibf$, as schematically shown in the figure. The work done by the system along the paths $af$, $ib$ and $bf$ are $W_{af}=200$ J, $W_{ib}=50$ J and $W_{bf}=100$ J respectively. The heat supplied to the system along the path $iaf$, $ib$ and $bf$ are $Q_{iaf}$, $Q_{ib}$ and $Q_{bf}$ respectively. If the internal energy of the system in the state $b$ is $U_b=200$ J and $Q_{iaf}=500$ J, the ratio $Q_{bf}/Q_{ib}$ is

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly : ($R=8.3$ JK$^{-1}$ mol$^{-1}$)

A gas is compressed from a volume of 2 m$^3$ to a volume of 1 m$^3$ at a constant pressure of 100 N/m$^2$. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

The figure shows the $P$-$V$ plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II.

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.