What amount of heat must be supplied to \(2.0\times 10^{-2}~\text{kg}\) of nitrogen (at room temperature) to raise its temperature by \(45~^{\circ}\text{C}\) at constant pressure? (Molecular mass of \(N_2 =28,\) \(R= 8.314~\text{J mol}^{-1}\text{K}^{-1}\)${\mathrm{}}^{}$).
1. \(935~\text{J}\)
2. \(934~\text{J}\)
3. \(936~\text{J}\)
4. \(930~\text{J}\)

A cylinder with a movable piston contains \(3\) moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

In changing the state of a gas adiabatically from an equilibrium state \(A\) to another equilibrium state \(B\), an amount of work equal to \(22.3~\mathrm{J}\) is done on the system. If the gas is taken from state \(A\) to \(B\) via a process in which the net heat absorbed by the system is \(9.35~\mathrm{cal}\), the net work done by the system in the latter case is approximately:
(Take \(1~\mathrm{cal}=4.2~\mathrm{J} \))
1. \(15~\mathrm{J}\) 
2. \(20~\mathrm{J}\) 
3. \(14~\mathrm{J}\) 
4. \(17~\mathrm{J}\) 

Two cylinders, A and B, of equal capacity are connected to each other via a stopcock. A contains gas at a standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. If the stopcock is suddenly opened, then the change in internal energy of the gas is:

An electric heater supplies heat to a system at a rate of \(100~\text{W}\). If the system performs work at a rate of \(75~\text{J/s}\). At what rate is the internal energy increasing?
1. \(20~\text{W}\)
2. \(25~\text{W}\)
3. \(29~\text{W}\)
4. \(27~\text{W}\)

A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in the figure. Its volume is then reduced to the original value from \(\mathrm{E}\) to \(\mathrm{F}\) by an isobaric process. The total work done by the gas from \(\mathrm{D}\) to \(\mathrm{E}\) to \(\mathrm{F}\) is:

  
1. \(600\) J
2. \(300\) J
3. \(450\) J
4. \(500\) J