Thermodynamics

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__________.

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

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

Which one of the following options is the correct combination?

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :

(Take $C_v=1.5$ R, where R is gas constant)

For the P-V diagram given for an ideal gas,

out of the following which one correctly represents the T-P diagram ?

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

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $PV^n$ = constant, then n is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively) :

'n' moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be :

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) :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

A Carnot freezer takes heat from water at 0°C inside it and rejects it to the room at a temperature of 27°C. The latent heat of ice is $336\times10^3$ J kg$^{-1}$. If 5 kg of water at 0°C is converted into ice at 0°C by the freezer, then the energy consumed by the freezer is close to :

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)

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\dfrac UV\propto T^4$ and pressure $p=\dfrac13\left(\dfrac UV\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is :

A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways :

(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.

(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.

In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is :

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$, where V is the volume of the gas. The value of q is :
$$\left(\gamma=\frac{C_p}{C_v}\right)$$

An ideal gas goes through a reversible cycle a→b→c→d has the V - T diagram shown below. Process d→a and b→c are adiabatic.

The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

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