4. The First Law of Thermodynamics for Closed Systems

Which statement correctly describes the fundamental difference between internal energy, heat, and work in thermodynamics?

What is the common sign convention used for heat (Q) and work (W) in the first law of thermodynamics for a closed system?

For a closed system undergoing a process where changes in kinetic and potential energies are negligible, how is the first law of thermodynamics expressed?

For an ideal gas, what is the primary factor that determines its specific internal energy (u)?

What is the total change in internal energy (ΔU) for any system that undergoes a complete thermodynamic cycle?

A closed, rigid tank contains 0.5 kg of nitrogen gas, which is treated as an ideal gas. The gas is heated, causing its temperature to rise from 10 C to 50 C. If the constant-volume specific heat (Cv) of nitrogen is 0.743 kJ/kgK, what is the change in the internal energy (ΔU) of the nitrogen?

Two kilograms of air, treated as an ideal gas, are heated from 10 C to 40 C. According to the principles for ideal gases, how does the change in internal energy (ΔU) for this process depend on whether the process is isochoric (constant volume) or isobaric (constant pressure)?

How is constant-volume specific heat (Cv) mathematically defined?

In a thermodynamic analysis problem involving a pure substance like water, when is it most appropriate to use thermodynamic tables to find the specific internal energy (u) instead of the ideal gas approximation Δu = CvΔT?

A closed system contains water at a pressure of 500 kPa and a temperature of 60 C. Given that the saturation pressure of water at 60 C is 19.95 kPa, what is the phase of the water and how would its specific internal energy (u) be found?

How is boundary work graphically represented in a thermodynamic process?

A rigid, sealed tank containing nitrogen gas is heated, causing the pressure and temperature to increase. What is the boundary work done by the nitrogen during this process?

A piston-cylinder device contains 0.2 kg of ammonia. It undergoes an isobaric (constant pressure) expansion at 100 kPa from an initial specific volume of 1.31365 m3/kg to a final specific volume of 1.46562 m3/kg. Calculate the boundary work done during this process.

Air, treated as an ideal gas, undergoes an isothermal expansion at a constant temperature of 50 C. The pressure drops from 200 kPa to 100 kPa. The gas constant for air is 0.287 kJ/kgK. Calculate the specific boundary work (w) done by the air.

What is the correct formula for calculating the boundary work (W) for a polytropic process (where PV^n = constant) between state 1 and state 2, assuming the polytropic exponent n is not equal to 1?

An ideal gas undergoes a polytropic expansion with n = 1.3 from an initial state of P1=200 kPa, v1=0.05 m3/kg to a final state where P2 = 81.225 kPa and v2=0.1 m3/kg. Calculate the specific boundary work (w) for this process.

For an ideal gas undergoing an isobaric (constant pressure) process, what is the value of the polytropic exponent 'n' in the relation Pv^n = constant?

An isothermal process for an ideal gas is described by the relation T = constant. How can this be expressed in the polytropic form Pv^n = constant?

What is the formula for the work done by a linear spring when it is compressed or expanded from an initial displacement x1 to a final displacement x2, measured from its rest position?

A linear spring with a spring constant K = 100 kN/m is initially uncompressed (x1 = 0 m). Gas in a piston-cylinder device expands, compressing the spring to a final displacement of x2 = 0.5 m. What is the total work done on the spring?

In a piston-cylinder device with a linear spring mounted on the piston, how does the gas pressure (P_gas) relate to the gas volume (V) during a quasi-equilibrium expansion or compression process?

For a process occurring in a closed, rigid tank, how does the first law of thermodynamics (ΔU = Q - W) simplify?

A closed, rigid tank has a constant volume and contains a gas. The process involves 15.9 kJ of heat being transferred to the gas. What is the change in the internal energy (ΔU) of the gas?

For a vapor compression refrigeration cycle, which operates as a closed system, what is the relationship between the heat absorbed from the cold space (QL), the heat rejected to the hot space (QH), and the work input to the compressor (Win)?

In an isobaric (constant pressure) expansion process of an ideal gas, how does the heat transferred (Q) relate to the change in internal energy (ΔU) and work done (W)?

A closed system undergoes a process where its internal energy decreases by 50 kJ. During this process, 20 kJ of work is done on the system. What is the heat transfer (Q) for this process?

In a compression process shown on a P-v diagram, the specific boundary work is negative. Why?

For a pure substance such as R134a at 40 C, its specific volume is found to be 0.1 m3/kg. The saturated vapor specific volume (vg) at 40 C is 0.019966 m3/kg. What is the phase of the R134a?

The total energy of a closed system is expressed as E = U + KE + PE. What does the term 'U' represent?

An ideal gas undergoes an isothermal expansion. Which statement correctly describes the energy changes according to the first law (ΔU = Q - W)?

What is specific heat transfer (q)?

A piston-cylinder device contains 0.5 kg of steam. The steam is cooled in a two-step process. In the first step (1 to 2), it is cooled isobarically at 200 kPa. In the second step (2 to 3), it is cooled isochorically to a final pressure of 25 kPa. The specific internal energies are u1 = 2654.63 kJ/kg and u3 = 272.10 kJ/kg. The total specific work done during the entire process (1 to 3) is -215.88 kJ/kg. Calculate the specific heat transfer (q) for the entire process.

For a polytropic process where the exponent n = infinity, what type of process does this represent?

The change in specific internal energy for ANY process involving an ideal gas can be found from what formula?

A piston-cylinder device contains gas that expands from an initial state to a final state via three different paths: A, B, and C. Which statement is true regarding the boundary work (W) and the change in internal energy (ΔU) for these three paths?

Why is heat transfer considered a 'boundary phenomenon'?

What condition is necessary for heat transfer to occur between a system and its surroundings?

An adiabatic process is one in which:

In the context of a piston-cylinder device with a spring, the total work done by the expanding gas is the sum of what two components?

The formula Δu = Cv(T2 - T1) is used for ideal gases. What is a key assumption about Cv in this formula for it to be accurate over a temperature range?

A gas in a piston-cylinder undergoes an isobaric expansion at 100 kPa. The initial and final specific internal energies are u1 = 1504.29 kJ/kg and u2 = 1554.1 kJ/kg. The total boundary work done is 3.039 kJ for the 0.2 kg of gas. Calculate the total heat transfer (Q) for this process.

Work associated with the expansion and compression of a gas is commonly called what?

Ammonia in a piston-cylinder is compressed in a polytropic process with n=1.25 from P1=100 kPa to P2=150 kPa. The mass is 0.5 kg. The initial and final states are (v1=1.31365 m3/kg, u1=1504.29 kJ/kg) and (v2=0.94974 m3/kg, u2=1540.82 kJ/kg). Calculate the heat transfer (Q) for this process.

A gas expands in a process where PV^1.3 = constant. This is an example of what type of process?

If a process is adiabatic, what is the value of Q, and how does the first law of thermodynamics simplify?

A linear spring has a spring constant K. What is the force, F, required to hold the spring at a displacement, x, from its rest position?

In a piston-cylinder device, a gas expands from V1 = 0.15 m3 to V2 = 0.2 m3. This expansion occurs against a linear spring and a constant atmospheric pressure. The gas pressure is found to vary linearly from P1 = 100 kPa to P2 = 600 kPa. Calculate the total work done by the gas.

What does the first law of thermodynamics state about 'perpetual-motion machines'?

When is it appropriate to use thermodynamic tables for a pure substance to determine its state and properties?

A closed system containing an ideal gas undergoes a process where no work is done (W=0), and its internal energy increases by 100 kJ. What can be concluded about the heat transfer (Q)?