Thermodynamics

Read the following statements :

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1:1.15.

C. A Carnot Engine working between 100K and 400K has an efficiency of 75%.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

In 1$^{\text{st}}$ case, Carnot engine operates between temperatures 300 K and 100 K. In 2$^{\text{nd}}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2$^{\text{nd}}$ case) will be :

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be :

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

The pressure P$_1$ and density d$_1$ of diatomic gas $\left(\gamma=\dfrac75\right)$ changes suddenly to P$_2$ (> P$_1$) and d$_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes _______ times of its initial temperature. (given $\dfrac{d_2}{d_1}=32$)

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

A Carnot engine is operating between the two reservoirs of temperature 227 °C and 127 °C respectively. If the engine performs $1.04\times10^5$ J work per cycle. Then, the heat absorbed from hot reservoir per cycle will be :

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below. During this cycle, heat is absorbed by the gas in

The value of $\dfrac{T_R}{T_0}$ is

The value of $\dfrac{Q}{RT_0}$ is

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A → B : Isothermal expansion at temperature T so that the volume is doubled from V$_1$ to V$_2$ = 2V$_1$ and pressure changes from P$_1$ to P$_2$.

B → C : Isobaric compression at pressure P$_2$ to initial volume V$_1$.

C → A : Isochoric change leading to change of pressure from P$_2$ to P$_1$.

Total workdone in the complete cycle ABCA is :

Match List I with List II.

Choose the correct answer from the options given below :

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4V_1$. After this, the gas expands adiabatically and its volume becomes $32V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{iso}$ and $W_{adia}$, respectively. If the ratio $\dfrac{W_{iso}}{W_{adia}} = f\ln 2$, then $f$ is ______.

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be ______ (take the acceleration due to gravity $= 10\ \mathrm{m\,s^{-2}}$ and the universal gas constant $= 8.3\ \mathrm{J\,mol^{-1}K^{-1}}$).

A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R - a)$. For $a \ll R$ the magnitude of the work done in the process is given by $(4\pi p_0 R a^2)X$, where $X$ is a constant and $\gamma = C_p/C_V = 41/30$. The value of $X$ is ______.

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature $(V$-$T)$ diagram. The correct statement(s) is/are:

[$R$ is the gas constant]

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure $P_0$, volume $V_0$, and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0/4$, then the correct statement(s) is/are,

(Given $2^{1.2} = 2.3$; $2^{3.2} = 9.2$; $R$ is gas constant)

If the process carried out on one mole of monatomic ideal gas is as shown in figure in the $PV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

If the process on one mole of monatomic ideal gas is as shown in the $TV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?