Question 4.2: A cylinder closed by a piston contains N moles of a diatomic...

Principles of Thermodynamics [EXP-7769]

A cylinder closed by a piston contains N moles of a diatomic gas characterised by U = (5/2) NRT and by pV = NRT, as in exercise 4.1. The gas has a temperature T when it is brought in contact with a heat reservoir at temperature $T_{ext}$ , causing an irreversible process to occur. The pressure p of the gas is equal to the constant pressure $p_{ext}$ of the environment at all times, i.e. $p = p_{ext} = const$ . Determine the amount of heat exchanged.

Numerical Application:

N = 0.5 mol, T = 450 K and $T_{ext}$ = 300 K.

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

The enthalpy of the gas is given by,

$H = U + p V = \frac{5}{2} N R T + N R T = \frac{7}{2} N R T$ .

According to the relation (4.61), the heat exchanged yields,

$Q_{if }= ΔH_{if}$ . (4.61)

$Q_{if} = ΔH_{if} = \frac{7}{2} N R (T_f − T_i) = 2.18$ k J.

Related Answered Questions

An open system consists of a fluid of a single substance kept between two pistons sliding inside a cylinder with adiabatic walls. Matter enters and exits the cylinder in two specific locations. These two matter flows generate a chemical power PC. The pressure at the entrance is p+ and the pressure

Verified Answer:

The rates of variation of substance and of volume ...

An state of an elastic rod is described by the state variables entropy S and length L. The differential of the internal energy U(S, L) of the rod is written as,dU = (∂U(S, L)/∂S) dS +(∂U(S, L)/∂L)dL = T (S, L) dS + f (S, L) dL ,Note that f (S, L) has the units of a force. The longitudinal

Verified Answer:

a) Applying the cyclic rule (4.81) to the force F ...

A system consists of a thin film of surface area A, of internal energy U(S, A), where dU = TdS + γ dA Hence, the surface tension is given by γ (S, A) = ∂U(S, A)/∂A Express the heat Qif to provide to the film for a variation ΔAif = Af − Ai of the surface of the film through an isothermal

Verified Answer:

Perform a Legendre transformation on the internal ...

a) Show that U (S, V) = − T^2 ∂/∂T(F (T, V)/T)where T ≡ T (S, V) is to be understood as a function of S and V. b) Show that H (S, p) = − T^2 ∂/∂T(G (T, p)/T)where T ≡ T (S, p) is to be understood as a function of S and p.

Verified Answer:

a) The internal energy U is related to the free en...

Determine the hydrostatic pressure p inside a droplet, as a function of its radius r (Fig. 4.1). Assume that the drop (d) forms at the end of a short thin tube mounted at the end of vertical cylindrer containing the liquid (l). When a drop forms at the end of the tube, the change in the container

Verified Answer:

The pressure difference is obtained by performing ...

Two of the Massieu functions are functions of the following state variables:1. J(1/T, V) 2. Y (1/T,/pT) The Massieu functions are obtained by performing Legendre transformations of the state function entropy S (U, V) with respect to the state variables U and V. Use Legendre transformations to

Verified Answer:

The entropy S (U, V) as a state function reads, [l...

The grand potential Φ(T, V, {μA}), also known as the Landau free energy, is a thermodynamical potential obtained by performing Legendre transformations of the internal energy U(S, V, {NA}). Use Legendre transformations to express the thermodynamical potential Φ(T, V, {μA}) in terms of the

Verified Answer:

To obtain the grand potential

Φ(T, V, \{μ_A...

Establish the expression of the differential of the internal energy dU(S (T, V) , V)as a function of the temperature T and the volume V. In the particular case of a gas that satisfies the relation pV = NR T, show that dU (S (T, V) , V) is proportional to dT.

Verified Answer:

According to the mathematical definition (4.76), t...

A soap bubble is a system consisting of two subsystems. Subsystem (f) is the thin film and subsystem (g) is the gas enclosed inside the film. The surrounding air is a thermal bath. The equilibrium is characterised by the minimum of the free energy F of the system. The differential of the free

Verified Answer:

Since the surrounding air is a thermal bath, the t...

A gas is characterised by the enthalpy H(S, p) = Cp T, where Cp is a constant (called heat capacity and defined in § 5.2), and by pV = NR T, where p is its pressure, V its volume, T its temperature and N the number of moles of gas. An adiabatic reversible compression brings the pressure from p1 to

Verified Answer:

For a reversible adiabatic process, we have dS = 0...