Thermodynamics PYQ — Page 4

Certain quantity of water cools from ${70 }^{o}C$ to ${60 }^{o}C$ in the first $5$ minutes and to ${54 }^{o}C$ in the next $5$ minutes. The temperature of the surroundings is:

The mean free path of molecules of a gas (radius ‘ $r$ ’) is inversely proportional to:

A monoatomic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V.$ The final pressure of the gas is: (take $\gamma =5/3$)

Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and crosssectional areas $A_1$ and $A_2$ respectively. If the rate of heat conduction in 1 is four times that in 2 , then:

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is

Two Carnot engines $\mathrm{A}$ and $\mathrm{B}$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $\mathrm{B}$ receives the heat at temperature $\mathrm{T}$ and rejects to its sink at temperature $T_2$. For what value of $T$ the efficiencies of the two engines are equal:

The amount of heat energy required to raise the temperature of 1 g of helium at NTP, from $T_1 \mathrm{~K}$ to $T_2 \mathrm{~K}$ is

Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning?

A piece of iron is heated in a flame. If first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

A gas is taken through the cycle $A \rightarrow B \rightarrow C \rightarrow A$, as shown. What is the net work done by the gas? 

The density of water at $20^{\circ} \mathrm{C}$ in $998 \mathrm{~kg} / \mathrm{m}^3$ and at a $40^{\circ} \mathrm{C} 992 \mathrm{~kg} / \mathrm{m}^3$. The cocfficient of volume expansion of water is:

In a vessel, the gas is at pressure $P$, if the mass of all the molecules is halved of their speed is double, then the resultant pressure will be :

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_V$ respectively. If $\gamma=\frac{C_p}{C_V}$ and $R$ is the universal gas constant, then $C_V$ is equal to

In the given ( $V-T)$ diagram, what is the relation between pressures $p_1$ and $p_2$ ? 

A system is taken from state a to state $c$ by two paths $a d c$ and $a b c$ as shown in the figure. The internal energy a is $U_2=10$ J. Along the path adc the amount of heat heat absorbed $\delta Q_1=50 \mathrm{~J}$ and the work obtained $\delta W_1=20 \mathrm{~J}$ whereas along the path $a b c$ the heat absorbed $\delta Q_2=36 \mathrm{~J}$. The amount of work along the path $a b c$ is: 

A thermodynamic system is taken through the cycle $A B C D$ as shown in figure. Heat rejected by the gas during the cycle is 

If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q$ ? ( $\sigma$ stands for Stefan's constant.)

Liquid oxygen at $50 \mathrm{~K}$ is heated to $300 \mathrm{~K}$ at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

An ideal gas goes from state $A$ to state $B$ via three different processes as indicated in the $p-V$ diagram If $Q_1, Q_2, Q_3$ indicate the heat absorbed by the gas along the three processes and $\Delta U_1, \Delta U_2, \Delta U_3$ indicate the change in internal energy along the three processes respectively, then 

A slab of stone of area of $0.36 \mathrm{~m}^2$ and thickness $0.1 \mathrm{~m}$ is exposed on the lower surface to steam at $100^{\circ} \mathrm{C}$. A block of ice at $0^{\circ} \mathrm{C}$ rests on the upper surface of the slab. In one hour $4.8 \mathrm{~kg}$ of ice is melted. The thermal conductivity of slab is (Given latent heat of fusion of ice $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ )

One mole of an ideal gas goes from an initial state $A$ to final state $B$ via two processes. It first undergoes isothermal expansion from volume $V$ to $3 V$ and then its volume is reduced from $3 V$ to $V$ at constant pressure. The correct $p-V$ diagram representing the two processes is

During an isothermal expansion, a confined ideal gas does $150 \mathrm{~J}$ of work against its surroundings. This implies that

When $1 \mathrm{~kg}$ of ice at $0^{\circ} \mathrm{C}$ melts to water at $0^{\circ} \mathrm{C}$, the resulting change in its entropy, taking latent heat of ice to be $80 \mathrm{cal} /{ }^{\circ} \mathrm{C}$, is

A mass of diatomic gas $(\gamma=1.4)$ at a pressure of $2 \mathrm{~atm}$ is compressed adiabatically so that its temperature rise from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The pressure of the gas is final state is