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Ksju [112]
3 years ago
14

One mole of a gas is placed in a closed system with a 20 L vessel initially at T = 300 K. The vessel is then isothermally expand

ed to 40 L. The gas follows the equation of state: P = RT/V + a/V2 where a = 240 L2 · atm/mol2 and R = 0.08206 L · atm/ mol · K. A. Derive an expression relating (dH/dV)T to measurable properties. B. Find DH for the gas in this process.
Physics
1 answer:
Elden [556K]3 years ago
8 0

Answer:

Given that

P = RT/V + a/V²

We know that

H= U + PV

For T= Constant  (ΔU=0)

ΔH= ΔU +Δ( PV)

ΔH= Δ( PV)

P = RT/V + a/V²

P V= RT + a/V

dH/dV = d(RT + a/V)/dV

dH/dV = - a/V²

So the expression of dH/dV

\dfrac{dH}{dV}=\dfrac{-a}{V^2}

b)

In isothermal process

\Delta H=nRT\ln{\dfrac{V_2}{V_1}}      (ΔU=0)

Now by putting the all values

\Delta H=nRT\ln{\dfrac{V_2}{V_1}}

\Delta H=1\times 0.08206\times 300\ln{\dfrac{40}{20}}

ΔH = 17.06 L.atm

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A student measured the mass of ice in a glass container with a tight lid. He allowed the ice to melt, and then found the mass of
vfiekz [6]

Answer:

The liquid formed from a melted solid has the same mass as the solid has.

Explanation:

As long as no water can escape, the mass of the ice before melting must equal the mass of the liquid water after.

7 0
3 years ago
A. How many atoms of helium gas fill a spherical balloon of diameter 29.6 cm at 19.0°C and 1.00 atm? b. What is the average kine
Korolek [52]

Answer:

a) 3.39 × 10²³ atoms

b) 6.04 × 10⁻²¹ J

c) 1349.35 m/s

Explanation:

Given:

Diameter of the balloon, d = 29.6 cm = 0.296 m

Temperature, T = 19.0° C = 19 + 273 = 292 K

Pressure, P = 1.00 atm = 1.013 × 10⁵ Pa

Volume of the balloon = \frac{4}{3}\pi(\frac{d}{2})^3

or

Volume of the balloon = \frac{4}{3}\pi(\frac{0.296}{2})^3

or

Volume of the balloon, V = 0.0135 m³

Now,

From the relation,

PV = nRT

where,

n is the number of moles

R is the ideal gas constant = 8.314  kg⋅m²/s²⋅K⋅mol

on substituting the respective values, we get

1.013 × 10⁵ × 0.0135 = n × 8.314 × 292

or

n = 0.563

1 mol = 6.022 × 10²³ atoms

Thus,

0.563 moles will have = 0.563 × 6.022 × 10²³ atoms = 3.39 × 10²³ atoms

b) Average kinetic energy = \frac{3}{2}\times K_BT

where,

Boltzmann constant, K_B=1.3807\times10^{-23}J/K

Average kinetic energy = \frac{3}{2}\times1.3807\times10^{-23}\times292

or

Average kinetic energy = 6.04 × 10⁻²¹ J

c) rms speed = \frac{3RT}{m}

where, m is the molar mass of the Helium = 0.004 Kg

or

rms speed = \frac{3\times8.314\times292}{0.004}

or

rms speed = 1349.35 m/s

5 0
3 years ago
A human being can be electrocuted if a current as small as 55 mA passes near the heart. An electrician working with sweaty hands
evablogger [386]

Answer:

The lethal voltage for the electrician under those conditions is 126.5 V.

Explanation:

To discover what is the lethal voltage to the electrician we need to find out what is the voltage that produces 55 mA = 0.055 A when across a resistance of 2300 Ohms (Electrician's body resistancy). For that we'll use Ohm's Law wich is expressed by the following equation:

V = i*R

Where V is the voltage we want to find out, i is the current wich is lethal to the electrician and R is his body resistance. By applying the given values we have:

V = 0.055*2300 = 126.5 V.

The lethal voltage for the electrician under those conditions is 126.5 V.

4 0
3 years ago
Read 2 more answers
At the surface of Jupiter's moon Io, the acceleration due to gravity is 1.81 m/s2 . A watermelon has a weight of 54.0 N at the s
butalik [34]

Answer:

m=5.51Kg

Explanation:

The weight of an object on Earth is given by W=mg, so we can calculate its mass by doing m=W/g, which for our values is:

m=(54N)/(9.8m/s^2)=5.51Kg

<em>Nothing is being asked</em> about Io but if one wanted to know the weight <em>W'</em> of the watermelon there one just have to do:

W'=ma=(5.51Kg)(1.81m/s^2)=9.97N

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3 years ago
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11111nata11111 [884]
The acceleration of a body in a gravitational field is independent of its mass. Both the stones will fall with the same acceleration through the same height and hence they will strike the ground simultaneously.
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