The temperature of 1 mole of an ideal monoatomic gas is increased by 50∘C at constant pressure. The total heat added and change in internal energy are E1 and E2, respectively. If E2E1=9x then the value of x is _____
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An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = $ constant. The coefficient of volume expansion of the gas is _______.
In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2)^{2}=4 a p$ where $a$ is a constant. The total work done in the closed path is 
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A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ} \mathrm{C}$. The gas is now heated to double its temperature. The modified pressure is $\_\_\_\_$ Pa. Note: Volume is constant.
A cylindrical tube $A B$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $A B$ and passing through the edge at end $A$, as shown in the figure. If $P_{A}$ and $P_{B}$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube) 
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