An ideal monoatomic gas undergoes a process such that its internal energy relates to the volume as $U=a\sqrt{V}$, where $a$ is a constant. Molar specific heat of the gas is $nR.$ Value of $n,$ is

A cyclic process $ABC$ is performed on one mole of an ideal gas, $T_A=350 \mathrm{K}$ and $T_B=450 \mathrm{K}$. A total of $1200 \mathrm{J}$ of heat is withdrawn from the gas in the complete cycle. Work done by the gas during process $B\to C$ is $-45n \mathrm{J}$. Value of $n$ is $\left[R=8.25{\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}\right]$

One mole of a monatomic gas undergoes the process $A\to B$ in the given $P-V$ diagram. The molar specific heat for the process is $\frac{nR}{16}$. Value of $n$, is

An ideal gas expands from a volume $V_0=1$ litre and pressure $P_0=1$ bar to volume $3$ litre along two different paths $ABC$ and $AC$ as shown in figure. The heat added to the gas along the path $ABC$ is $600 \mathrm{J}$. The heat transfer in the process along the path $AC$ is $10n \mathrm{J}$. Value of $n$, is

Six moles of an ideal gas performs a cycle shown in figure. If temperatures are $T_A=600 \mathrm{K},T_B=800 \mathrm{K}$ and $T_D=1200 \mathrm{K}$, the temperature at point $\mathrm{C}\left(\mathrm{in} \mathrm{K}\right)$, is $40 n$. Value of $n$, is