$100 \mathrm{g}$ of water is heated from $30 °\mathrm{C}$ to $50 °\mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (Specific heat of water is $4184 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

The figure shows the $pV$-plot of an ideal gas taken though a cycle $ABCDA$. (Fig. $20.53$) The part $ABC$ is a semi-circle and $CDA$) is half of an ellipse. Then

One mole of an ideal gas having initial volume $V$, pressure $2p$ and temperature $T$ under goes a cyclic process $ABCDA$ as shown in figure, The net work done in the complete cycle is

When a system is taken from state $i$ to state $f$ along the path $iaf$, then found that $Q=50 \mathrm{cal}$ and $W=20 \mathrm{cal}$. Along the path $ibf$,$\mathrm{Q}=36 \mathrm{cal}. \mathrm{W}$ along the path $ibf$ is

The $p-V$, diagram of a gas undergoing a cyclic process $\left(ABCDA\right)$, is shown in the graph, where $p$, is in units of ${\mathrm{Nm}}^{-2}$ and $V$ in ${\mathrm{cm}}^3$. Identify the incorrect statement.

Find the amount of heat required to raise the temperature of the gas through the same range at constant volume, $310 \mathrm{J}$ of heat is required to raise the temperature of $2$ moles of an ideal gas at constant pressure from $25°\mathrm{C}$ to $35°\mathrm{C}$.

The $p-V$, diagram of $2 \mathrm{g}$, of helium gas for a certain process $A\to B$, is shown in the figure. What is the heat given to the gas during the process $A\to B$