Thermodynamics Test. 3

A state function (like internal energy, pressure, temperature, volume) depends only on the current state of the system, not on the path taken to reach that state.

Temperature is directly proportional to the average translational kinetic energy of the particles in a substance.

For a diatomic gas, Cᵥ = (5/2)R and Cₚ = (7/2)R, so γ = (7/2)R / (5/2)R = 7/5 = 1.4.

This equation states that the change in a system's internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W).

A path function (like heat and work) is a property that depends on the path taken to get from an initial to a final state.

This is the statement of the third law. At absolute zero, a perfect crystal has a minimum possible entropy, which is defined as zero.

An example is a pot of boiling water without a lid, which exchanges heat (energy) and water vapor (matter) with the air.

In an isochoric process, the volume is constant (ΔV=0). Since W = PΔV, no work is done.

An example is a sealed can of soup being heated. It can absorb heat (energy) but no matter can enter or leave.

First, convert temperatures to Kelvin: Tₕ = 327 + 273 = 600 K; T꜀ = 27 + 273 = 300 K. The efficiency (η) is calculated using the formula η = 1 - (T꜀ / Tₕ). So, η = 1 - (300 K / 600 K) = 1 - 0.5 = 0.5, which is 50%.

The coefficient of performance (COP) for a heat pump is the ratio of the desired output (heat delivered to the hot reservoir, Qh) to the required input (work done, W).

An example is a perfectly insulated thermos. It is an idealization as perfect isolation is not achievable in practice.

For a monatomic gas, Cᵥ = (3/2)R and Cₚ = (5/2)R, so γ = (5/2)R / (3/2)R = 5/3 ≈ 1.67.

The first law of thermodynamics (ΔU = Q - W) shows that the change in internal energy (ΔU) is the sum of heat added (Q) and work done on the system (-W).

The efficiency of a Carnot engine depends only on the absolute temperatures of the cold (Tc) and hot (Th) reservoirs.

In an isothermal process (ΔT=0), heat can be added without changing the temperature. Since C = Q/(mΔT), dividing by zero gives an infinite specific heat.

In an adiabatic process, there is no heat exchange (Q=0). Since C = Q/(mΔT), the specific heat is zero.

A Carnot cycle is a theoretical thermodynamic cycle consisting of four reversible steps: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

This is the definition of a reversible process, which is an idealization used in thermodynamics.

For a reversible process, the change in entropy (ΔS) is the heat transferred (ΔQ) divided by the absolute temperature (T) at which the transfer occurs.