State 1st Law of Thermodynamics ($\Delta Q = \Delta U + W$). In a process, $500\text{ J}$ of heat is supplied to a gas and it performs $200\text{ J}$ of work. Find change in internal energy.
2.
Derive expression for work done during an Isothermal expansion ($W = n R T \ln\left(\frac{V_2}{V_1}\right)$) and Adiabatic expansion ($W = \frac{P_1 V_1 - P_2 V_2}{\gamma - 1}$).
Section B: Heat Engines & Carnot Cycle
3.
Derive the efficiency of a Carnot Engine $\eta = 1 - \frac{T_2}{T_1}$. A Carnot engine operates between $500\text{ K}$ and $300\text{ K}$. Find its efficiency.
4.
State 2nd Law of Thermodynamics (Kelvin-Planck and Clausius statements).
