Grade 11 : Physics - Thermodynamics (Set 1)

Explanation: The Zeroth Law states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This enables the definition and measurement of temperature.

Explanation: According to the First Law of Thermodynamics: $$\Delta Q = \Delta U + W$$ Given $\Delta Q = +400\text{ J}$ and $W = +150\text{ J}$: $$\Delta U = \Delta Q - W = 400\text{ J} - 150\text{ J} = 250\text{ J}$$

Explanation: An isochoric process occurs at constant volume ($\,\Delta V = 0\,$). Since work done is given by $W = \int P dV$, when $\,\Delta V = 0\,$, the work done is strictly zero.

Explanation: Mayer's relation states that for one mole of an ideal gas, the difference between molar specific heat at constant pressure and constant volume is equal to the universal gas constant $R$: $$C_p - C_v = R$$

Explanation: According to Joule's law for ideal gases, internal energy is purely a function of absolute temperature $T$, as intermolecular potential forces are assumed to be zero ($U = U(T)$).

Explanation: An adiabatic process is one in which no heat energy enters or leaves the system across its boundaries ($\Delta Q = 0$).

Explanation: For an isobaric process, work done $W = P \Delta V$. $$\,\Delta V = 0.05 - 0.02 = 0.03\text{ m}^3$$ $$W = (2.0 \times 10^5\text{ Pa}) \times (0.03\text{ m}^3) = 6000\text{ J}$$

Explanation: Internal energy $U$ is a state function. For a complete cycle, the initial and final states are identical, so the net change $\Delta U = U_{\text{final}} - U_{\text{initial}} = 0$.

Explanation: For a monatomic gas, $C_v = \frac{3}{2}R$ and $C_p = \frac{5}{2}R$. Thus: $$\gamma = \frac{C_p}{C_v} = \frac{5/2}{3/2} = \frac{5}{3} \approx 1.67$$

Explanation: The Clausius statement establishes that heat cannot flow spontaneously from a body at a lower temperature to a body at a higher temperature without external work being performed.

Explanation: The efficiency of a Carnot engine is given by: $$\eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{600} = 1 - 0.5 = 0.5 = 50\%$$

Explanation: In an isothermal process, temperature $T$ remains constant ($\Delta T = 0$). Because the internal energy of an ideal gas depends only on temperature, $\Delta U = 0$.

Explanation: Heat required is calculated as: $$Q = m c \Delta T = (2\text{ kg}) \times (4186\text{ J/(kg}\cdot\text{K)}) \times 10\text{ K} = 83720\text{ J}$$

Explanation: Since work is defined as $W = \int P dV$, the area under the curve on a $P\text{--}V$ diagram directly represents the mechanical work done during the process.

Explanation: The governing equation for a reversible adiabatic process of an ideal gas is $P V^\gamma = \text{constant}$, where $\gamma = C_p / C_v$ is the adiabatic index.

Explanation: A rigid diatomic gas has 5 degrees of freedom ($f = 5$). Thus $C_v = \frac{5}{2}R$, $C_p = \frac{7}{2}R$, and $\gamma = \frac{7}{5} = 1.40$.

Explanation: By sign conventions: heat removed means $\Delta Q = -100\text{ J}$; work done on system means $W = -300\text{ J}$.$$\Delta U = \Delta Q - W = -100\text{ J} - (-300\text{ J}) = +200\text{ J}$$

Explanation: An isobaric process is a thermodynamic process in which the pressure $P$ of the system remains constant throughout ($P = \text{constant}$).

Explanation: A reversible process requires that the system remains in thermodynamic equilibrium at every intermediate state (quasi-static) and that no energy is dissipated by dissipative forces such as friction.

Explanation: The work done per cycle by a heat engine equals the net heat absorbed: $$W = Q_H - Q_C = 2000\text{ J} - 1200\text{ J} = 800\text{ J}$$