When $1 \ mol$ of ice melts at $0 \ ^oC$ and a constant pressure of $1 \ atm$,the system absorbs $1440 \ cal$ of heat. If the molar volumes of ice and water are $0.0196 \ L$ and $0.0180 \ L$ respectively,calculate the change in internal energy $(\Delta U)$ of the system in $cal$.

Two moles of an ideal gas are allowed to expand from a volume of $10 \ dm^3$ to $2 \ m^3$ at $300 \ K$ against a pressure of $101.325 \ kPa$. Calculate the work done. (in $kJ$)

If $3 \ mol$ of an ideal gas at $300 \ K$ expand isothermally from $30 \ dm^3$ to $45 \ dm^3$ against a constant opposing pressure of $80 \ kPa$,then the amount of heat transferred is . . . . . . $J$.

In an isobaric process,the ratio of heat supplied to the system $(dQ)$ and work done by the system $(dW)$ for a diatomic gas is:

Two vessels $A$ and $B$ are connected via a stopcock. Vessel $A$ is filled with a gas at a certain pressure. The entire assembly is immersed in water and allowed to reach thermal equilibrium. After opening the stopcock,the gas from vessel $A$ expands into vessel $B$,and no change in temperature is observed. Which of the following statements is true?

Express the change in internal energy of a system when
$(i)$ No heat is absorbed by the system from the surroundings,but work $(w)$ is done on the system. What type of wall does the system have?
$(ii)$ No work is done on the system,but $q$ amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
$(iii)$ $w$ amount of work is done by the system and $q$ amount of heat is supplied to the system. What type of system would it be?