The volume of a gas at pressure $21 \times {10^4}\,N/{m^2}$ and temperature $27^o C$ is $83 $ litres. If $R = 8.3\ J/mol/K$, then the quantity of gas in $gm-mole$ will be
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A hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with diameter of $11.7 \,m$ and the mass of the balloon and the payload (without the hot air inside) is $210 \,kg$. Temperature and pressure of outside air are $27^{\circ} C$ and $1 atm =10^5 \,N / m ^2$, respectively. Molar mass of dry air is $30 \,g$. The temperature of the hot air inside is close to .......... $^{\circ} C$ [The gas constant, $R=8.31 \,JK ^{-1} mol ^{-1}$ ]
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 )
Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1=4\ g$ and that of hydrogen $M_2=2\ g$ The equivalent molar mass of the mixture is
Two thermodynamical process are shown in the figure. The molar heat capacity for process $A$ and $B$ are $C_A$ and $C_B$. The molar heat capacity at constant pressure and constant volume are represented by $C_P$ and $C_V$, respectively. Choose the correct statement.
A fix amount of nitrogen gas ($1$ mole) is taken and is subjected to pressure and temperature variation. The experiment is performed at high pressure as well as high temperatures. The results obtained are shown in the figures. The correct variation of $PV/RT$ with $P$ will be exhibited by