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

Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A, B, C$ . Let $Q, W$ and $U$ represent the heat supplied to the gas, work done by the gas, and the internal energy of the gas, respectiely, then which of the following conditions is true?

A cyclic process $ABCA$ is shown in $PT$ diagram. When presented on $PV$, it would be

Two cylinders of equal size are filled with equal amount of ideal diatomic gas at room temperature. Both the cylinders are fitted with pistons. In cylinder A the piston is free to move while in $B$ position is fixed. When same amount of heat is supplied to both the cylinders, the temperature of the gas cylinder $A$ raises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B.$

$2$ moles of a diatomic gas undergoes the process : $PT_2/V$ = constant. Then, the molar heat capacity of the gas during the process will be equal to

An ideal gas heat engine operates in Carnot's cycle between $227\,^oC$ and $127\,^oC$ . It absorbs $6.0 \times 10^4\,cal$ at higher temperature. The amount of heat converted into work is equal to