Exercise 1

Match the List-I with List-II

Choose the correct answer from the options given below:

An ideal gas initially at $0°\mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is_____ $\mathrm{{\rm K}}$.

$$\begin{gathered} \mathrm{An} \mathrm{ideal} \mathrm{gas} \mathrm{goes} \mathrm{from} \mathrm{an} \mathrm{initial} \mathrm{state} \mathrm{to} \mathrm{final} \mathrm{state}. \mathrm{During} \mathrm{the} \mathrm{process}, \mathrm{the} \mathrm{pressure} \mathrm{of} \mathrm{gas} \mathrm{increases} \mathrm{linearly} \mathrm{with} \mathrm{temperature}. \\ \mathrm{A}. \mathrm{The} \mathrm{work} \mathrm{done} \mathrm{by} \mathrm{gas} \mathrm{during} \mathrm{the} \mathrm{process} \mathrm{is} \mathrm{zero}. \\ \mathrm{B}. \mathrm{The} \mathrm{heat} \mathrm{added} \mathrm{to} \mathrm{gas} \mathrm{is} \mathrm{different} \mathrm{from} \mathrm{change} \mathrm{in} \mathrm{its} \mathrm{internal} \mathrm{energy}. \\ \mathrm{C}. \mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{the} \mathrm{gas} \mathrm{is} \mathrm{increased}. \\ \mathrm{D}. \mathrm{The} \mathrm{internal} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{gas} \mathrm{is} \mathrm{increased}. \\ \mathrm{E}. \mathrm{The} \mathrm{process} \mathrm{is} \mathrm{isochoric} (\mathrm{constant} \mathrm{volume} \mathrm{process}) \\ \mathrm{Choose} \mathrm{the} \mathrm{correct} \mathrm{answer} \mathrm{from} \mathrm{the} \mathrm{options} \mathrm{given} \mathrm{below}:- \end{gathered}$$

Given below are two statements. One is labelled as
Assertion (A) and the other is labelled as
Reason(R).
Assertion (A): In an insulated container, a gas is
adiabatically shrunk to half of its initial volume.
The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an
irreversible and an adiabatic process.
In the light of the above statement, choose the
correct answer from the options given below:

$$\begin{gathered} The magnitude of heat exchanged by a system for \\ the given cyclic process ABCA (as shown in figure) is \\ (in SI unit) \end{gathered}$$

A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines – engine ${\mathrm{E}}_1$ works between 473 K to 373 K and engine ${\mathrm{E}}_2$ works between 373 K to 273 K. If ${\mathrm{\eta }}_{12}, {\mathrm{\eta }}_1$ and ${\mathrm{\eta }}_2$ are the efficiencies of the engines $\mathrm{E}, {\mathrm{E}}_1$ and ${\mathrm{E}}_2$ respectively, then

The workdone in an adiabatic change in an ideal gas depends upon only:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R): In isothermal process, PV = constant, while in adiabatic process PV = constant. Here y is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below: