A cycle tyre bursts suddenly. This represents an
Isothermal process
Isobaric process
Isochoric process
Adiabatic process
An ideal gas of density $\rho=0.2 kg m ^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=0.8 kg s ^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 m ^2$ and the upper end is $A_2=0.4 m ^2$. The pressure and the temperature of the gas at the lower end are $600 Pa$ and $300 K$, respectively, while its temperature at the upper end is $150 K$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 ms ^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure.
Which of the following statement($s$) is(are) correct?
This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process.
Statement $2 :$ The temperature of a gas remains constant in an adiabatic process.
At $N.T.P.$ one mole of diatomic gas is compressed adiabatically to half of its volume $\gamma = 1.41$. The work done on gas will be ....... $J$
A monatornic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2\, V$ and then adiabatically to a volume $16\, V.$ The final pressure of the gas is $(\,Take \,\gamma = 5/3)$
Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition