Thermodynamics

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

Which one of the following options is correct?

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma = \dfrac53$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{a2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$, respectively.

Which of the following statement(s) is(are) correct?

In the given $P$-$V$ diagram, a monoatomic gas $\left(\gamma = \frac53\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac13\right)^{0.6} \simeq 0.5$, $\ln 2 \simeq 0.7$].

Which of the following statement(s) is(are) correct?

A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ?

A Carnot engine takes 5000 kcal of heat from a reservoir at 727°C and gives heat to a sink at 127°C. The work done by the engine is

A monoatomic gas performs a work of $\dfrac Q4$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______ R during this transformation.

Where R is the gas constant.

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

(R = universal gas constant)

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ______ K.

In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If the workdone by the engine when it transfers heat from reservior to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is ______ $\times10^6$ J.

A diatomic gas ($\gamma=1.4$) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is ______ J.

Given below are two statements :

Statement I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state $(P_1,V_1,T_1)$ to state $(P_2,V_2,T_2)$, then work done is $W=\dfrac{\mu R(T_2-T_1)}{1-\gamma}$, where $\gamma=\dfrac{C_P}{C_V}$ and R = universal gas constant.

Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below:

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during the part CA is :

300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is 227°C, then the temperature of sink will be ______ °C.

Starting with the same initial conditions, an ideal gas expands from volume $V_1$ to $V_2$ in three different ways. The work done by the gas is $W_1$ if the process is purely isothermal, $W_2$, if the process is purely adiabatic and $W_3$ if the process is purely isobaric. Then, choose the correct option

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm$^3$ to 150 cm$^3$ adiabatically. In this process, the value of workdone on the gas will be :

A certain amount of gas of volume V at 27°C temperature and pressure $2\times10^7$ Nm$^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$) :

Let $\eta_1$ is the efficiency of an engine at $T_1=447$°C and $T_2=147$°C while $\eta_2$ is the efficiency at $T_1=947$°C and $T_2=47$°C. The ratio $\dfrac{\eta_1}{\eta_2}$ will be :

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40K at constant pressure. The increase in the internal energy of the gas in this process is :

(Given R = 8.3 JK$^{-1}$ mol$^{-1}$)

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :