Answer:
(a) 106 kPa
(b) 0.0377 mol
(c) 17.8 cm
Explanation:
(a) There are three forces on the piston. Atmospheric pressure pushing down, weight pulling down, and pressure of the gas pushing up.
∑F = ma
PA − mg − PₐA = 0
P = (PₐA + mg) / A
P = Pₐ + (mg / A)
P = 101,300 Pa + (40.0 N) / (π (0.05 m²))
P = 106,393 Pa
P = 106 kPa
(b) Use ideal gas law.
PV = nRT
(106,393 Pa) (π (0.05 m²) (0.11 m)) = n (8.314 Pa m³/mol/K) (20 + 273.15) K
n = 0.0377 mol
(c) Use ideal gas law to find the new volume of the gas.
PV = nRT
(106,393 Pa) (π (0.05 m²) h) = (0.0377 mol) (8.314 Pa m³/mol/K) (200 + 273.15) K
h = 0.178 m
h = 17.8 cm
Answer: 0.049 mol
Explanation:
1) Data:
n₁ = 0.250 mol
p₁ = 730 mmHg
p₂ = 1.15 atm
n₂ - n₁ = ?
2) Assumptions:
i) ideal gas equation: pV = nRT
ii) V and T constants.
3) Solution:
i) Since the temperature and the volume must be assumed constant, you can simplify the ideal gas equation into:
pV = nRT ⇒ p/n = RT/V ⇒ p/n = constant.
ii) Then p₁ / n₁ = p₂ / n₂
⇒ n₂ = p₂ n₁ / p₁
iii) n₂ = 1.15atm × 760 mmHg/atm × 0.250 mol / 730mmHg = 0.299 mol
iv) n₂ - n₁ = 0.299 mol - 0.250 mol = 0.049 mol
Answer:

Explanation:
As we know that the equation of particle position is given as

Now the speed of the particle is given as

now we know that potential energy and kinetic energy is equal
so we have

so we will have





