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 $\mathrm{N}_2 =28,$ $R= 8.314~\text{J mol}^{-1}\text{K}^{-1}$).
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?

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?

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