Practice Questions

Recall the relationship between the molar specific heat capacity at constant pressure ($C_p$) and at constant volume ($C_v$) for an ideal gas.

A thermodynamic system absorbs $200 \text{ J}$ of heat from its surroundings and performs $50 \text{ J}$ of work on the surroundings. Calculate the change in the internal energy of the system.

State the Zeroth Law of Thermodynamics.

Define the term 'internal energy' of a thermodynamic system.

For a cyclic process, the net work done by the system is found to be $500 \text{ J}$. Calculate the net heat supplied to the system during this process.

Justify why internal energy ($U$) is classified as an extensive state variable, while temperature ($T$) is classified as an intensive state variable.

List four types of thermodynamic processes and define one of them.

Apply the Zeroth Law of Thermodynamics to demonstrate how a thermometer is able to measure the temperature of another object.

Contrast extensive and intensive thermodynamic variables. Demonstrate their difference by providing two examples of each and considering a system divided into two equal parts.

For an ideal gas, the molar specific heat at constant volume is given as $C_v = 12.5 \text{ J mol}^{-1} \text{K}^{-1}$. Apply Mayer's relation to calculate its molar specific heat at constant pressure, $C_p$. (Use $R = 8.314 \text{ J mol}^{-1} \text{K}^{-1}$)

Critique the historical 'caloric theory' of heat from the perspective of modern thermodynamics, citing a key experiment that invalidated it.

A Carnot engine operates between a hot reservoir at a temperature of $527^{\circ}\text{C}$ and a cold reservoir at $127^{\circ}\text{C}$. Calculate its maximum possible efficiency. Analyze how the efficiency would change if the temperature of the cold reservoir were decreased to $27^{\circ}\text{C}$.

A thermodynamic system undergoes a process in which its internal energy decreases by $300 \text{ J}$. If $120 \text{ J}$ of work is done on the system during this process, solve for the amount of heat transferred and specify whether heat is added to or removed from the system.

An ideal gas with $\gamma = 1.4$ is compressed adiabatically from an initial pressure of $1 \times 10^5 \text{ Pa}$ and volume of $2.0 \text{ m}^3$ to a final volume of $0.5 \text{ m}^3$. Calculate the final pressure of the gas.

Analyze why the molar specific heat capacity of a gas at constant pressure ($C_p$) is always greater than its molar specific heat capacity at constant volume ($C_v$).

Evaluate the following statement: 'In a quasi-static adiabatic compression of an ideal gas, no heat is added to the system, therefore its temperature must remain constant.'

Justify the necessity of the Zeroth Law of Thermodynamics, given that it was formulated after the First and Second Laws. Why are the first two laws insufficient to rigorously define temperature?

Evaluate why a quasi-static process is a necessary idealization for a reversible process. Can a non-quasi-static process ever be reversible? Justify your answer.

Justify why the work done ($W$) by a gas during a quasi-static expansion from state A to state B is a path-dependent function, while the change in its internal energy ($\Delta U$) is path-independent.

Recall the mathematical expression for the First Law of Thermodynamics and explain each term.

State the Kelvin-Planck statement of the Second Law of Thermodynamics.

Explain the difference between an adiabatic wall and a diathermic wall.

A system is supplied with $200 \text{ J}$ of heat, and the system performs $80 \text{ J}$ of work on its surroundings. Recall the First Law of Thermodynamics to find the change in the internal energy of the system.

Compare the pressure-volume (P-V) curves for isothermal and adiabatic expansions of an ideal gas, starting from the same initial state $(P_1, V_1)$. Analyze which process results in a lower final pressure for the same final volume.

Two moles of an ideal gas expand isothermally from an initial volume of $10 \text{ L}$ to a final volume of $25 \text{ L}$ at a constant temperature of $300 \text{ K}$. Calculate the work done by the gas during this expansion. (Use the universal gas constant $R = 8.314 \text{ J mol}^{-1} \text{K}^{-1}$)

Analyze why heat and work are considered path functions, not state variables in thermodynamics.

Explain the concepts of extensive and intensive state variables, providing two examples for each.

State the Clausius statement of the Second Law of Thermodynamics.

An ideal gas undergoes an adiabatic expansion where the work done by the gas is $250 \text{ J}$. Identify the change in heat supplied and the change in internal energy of the gas.

A student claims to have invented a device that cools a room by absorbing heat and converting it entirely into work, without releasing any heat to a hotter reservoir. Critique this claim using the laws of thermodynamics.

Recall the formula for the work done by an ideal gas during an isothermal expansion from volume $V_1$ to $V_2$ at a constant temperature $T$.

Formulate a real-world example of an irreversible process. Propose how this process could be idealized as a reversible one and critique the limitations of this idealization.

An inventor claims to have built a heat engine that operates in a cycle between a source at $500 \text{ K}$ and a sink at $300 \text{ K}$. The engine allegedly receives $1000 \text{ J}$ of heat from the source and produces $500 \text{ J}$ of work in each cycle. Evaluate this claim by comparing its efficiency to the maximum possible theoretical efficiency.

A system containing 1 mole of an ideal monatomic gas undergoes a rectangular cyclic process A → B → C → D → A on a P-V diagram. The coordinates are A($V_0, P_0$), B($2V_0, P_0$), C($2V_0, 2P_0$), and D($V_0, 2P_0$). Create a labeled P-V diagram for this process and evaluate the total work done by the gas, the net heat absorbed, and the total change in internal energy over one complete cycle.

A Carnot engine absorbs $6.0 \times 10^5 \text{ J}$ of heat from a source at $627^{\circ}\text{C}$ and rejects heat to a sink at $27^{\circ}\text{C}$. Calculate the efficiency of the engine, the work done by the engine, and the amount of heat rejected to the sink.

Summarize the four processes that constitute a Carnot cycle, starting from the isothermal expansion.

Calculate the amount of heat required to raise the temperature of $3$ moles of a diatomic ideal gas by $20 \text{ K}$ at constant pressure. Assume the gas has a molar specific heat at constant volume of $C_v = \frac{5}{2}R$. (Use $R = 8.314 \text{ J mol}^{-1} \text{K}^{-1}$)

Design a hypothetical thermodynamic cycle for an ideal gas that consists of four processes in a sequence: isobaric expansion, isochoric cooling, isobaric compression, and isochoric heating, returning the gas to its initial state. Formulate expressions for the net work done and the efficiency of this cycle in terms of initial and final pressures and volumes.

Propose a simple experimental setup to justify that heat is a form of energy in transit and not a property of a system, distinguishing it from internal energy.

Explain why internal energy is considered a state variable, while heat and work are not.

Formulate a logical proof to justify why two distinct reversible adiabatic curves for an ideal gas cannot intersect on a P-V diagram.

Design a two-step process for an ideal gas that takes it from an initial state A to a final state B where the net heat supplied to the system is zero ($\Delta Q = 0$), but the process itself is not adiabatic. Justify that such a process is possible.

An engineer proposes to create a new heat engine cycle by replacing the two reversible adiabatic steps in a Carnot cycle with two constant-volume (isochoric) steps. Evaluate the efficiency of this new cycle compared to the Carnot cycle operating between the same two temperature reservoirs, $T_1$ and $T_2$.

Describe what is meant by a 'quasi-static' process in thermodynamics.

Examine the operation of a household refrigerator using the Clausius statement of the Second Law of Thermodynamics. Explain why the back of a working refrigerator feels warm and analyze why it is impossible to cool a room by leaving the refrigerator door open.