1.State Zeroth Law and First Law of Thermodynamics.
Sol: Zeroth Law defines temperature concept. First Law: $\Delta Q = \Delta U + W$.
2.Distinguish between Isothermal and Adiabatic processes.
Sol: Isothermal: Constant temperature ($T = \text{const}, \Delta U = 0$). Adiabatic: No heat transfer ($\Delta Q = 0$).
3.Write expression for work done during an isothermal expansion.
Sol: $W = n R T \ln\left(\frac{V_2}{V_1}\right) = 2.303 n R T \log_{10}\left(\frac{V_2}{V_1}\right)$.
4.State efficiency formula for a Carnot engine.
Sol: $\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{Q_2}{Q_1}$.
5.In a process, $500 \text{ J}$ of heat is supplied to a system while it does $200 \text{ J}$ of work. Find change in internal energy.
Sol: $\Delta U = \Delta Q - W = 500 - 200 = 300 \text{ Joules}$.
6.Calculate work done when $2 \text{ moles}$ of ideal gas expand isothermally at $300 \text{ K}$ from $V$ to $2V$ ($R = 8.314 \text{ J/mol}\cdot\text{K}$).
Sol: $W = 2 \times 8.314 \times 300 \times \ln(2) = 4988.4 \times 0.693 = 3457 \text{ Joules}$.
7.Find efficiency of Carnot engine operating between $500 \text{ K}$ and $300 \text{ K}$.
Sol: $\eta = 1 - \frac{300}{500} = 1 - 0.6 = 0.4 = 40\%$.
8.A monoatomic gas ($\gamma = 5/3$) at STP is compressed adiabatically to $1/8^{\text{th}}$ of its initial volume. Find final pressure.
Sol: $P_2 V_2^\gamma = P_1 V_1^\gamma \implies P_2 = P_1 \left(\frac{V_1}{V_2}\right)^\gamma = 1 \text{ atm} \times (8)^{5/3} = 1 \times (2^3)^{5/3} = 2^5 = 32 \text{ atm}$.
