The P - V diagram of a system undergoing a thermodynamic process is shown in figure. Work done by the system in going from $A\to B\to C$ is 30 J and 40 J heat is given to the system. The change in internal energy of the gas if the gas is directly taken from A to C  is 

A vessel contains $N$ molecules of a gas at temperature $T$. Now the number of molecules is doubled, keeping the total energy in the vessel constant. The temperature of the gas is.

Which relation is correct for isochoric process

The temperature at the bottom of a high water fall is higher than that at the top because

A thermodynamical process is shown in the figure. The pressure and volumes corresponding to some points in the figure are$P_A=3\times {10}^{4}Pa$ $V_A=2\times {10}^{-3}{m}^3$$P_B=8\times {10}^{4}Pa$ $V_D=5\times {10}^{-3}{m}^3$In the process $AB$, $600J$ of heat is added to the system and in process $BC200J$ of heat is added to the system. The change in internal energy of the system in process $AC$ would be

Water of mass $m_2$ = 1 kg is contained in a copper calorimeter of mass $m_1$  = 1 kg. Their common temperature t = $10^{0}C$. Now a piece of ice of mass $m_3$  = 2 kg and temperature is $-11^{0}C$ dropped into the calorimeter. Neglecting any heat loss, the final temperature of system is. [specific heat of copper = 0.1 Kcal/ kg${}^{0}C$, specific heat of water = 1 Kcal/kg${}^{0}C$, specific heat of ice = 0.5 Kcal/kg${}^{0}C$, latent heat of fusion of ice = 78.7 Kcal/kg]

Which of the following parameters does not charaterize the thermodynamic state of matter?

One end of a $0.25m$ long metal bar is in steam and the other end is in contact with ice. If $12g$ of ice melts per minute, what is the thermal conductivity of the metal? Given cross-section of the bar $=5\times 10^{-4}{m}^2$ and latent heat of ice is $80cal/g$.

$C_v$ for ammonia gas is $(inJmo{l}^{-1}{K}^{-1})$

A liquid boils at such a temperature at which the saturated vapour pressure, as compared to atmospheric pressure, is