A mass of diatomic gas $(\gamma = 1 .4)$ at a pressure of $2$ atmospheres is compressed adiabatically so that its temperature rises from $27^o C$ to $927^o C.$ The pressure of the gas in the final state is  ...... $atm$

A gas may expand either adiabatically or isothermally. A number of $P-V$ curves are drawn for the two processes over different range of pressure and volume. It will be found that

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?

A certain amount of gas of volume $V$ at $27^{o}\,C$ temperature and pressure $2 \times 10^{7} \;Nm ^{-2}$ 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 $\gamma=1.5$ )

The work done in which of the following processes is equal to the internal energy of the system?

A gas at $NTP$ is suddenly compressed to one-fourth of its original volume. If $\gamma $ is supposed to be $\frac{3}{2}$, then the final pressure is........ atmosphere