Answer:
the work is done by the gas on the environment -is W= - 3534.94 J (since the initial pressure is lower than the atmospheric pressure , it needs external work to expand)
Explanation:
assuming ideal gas behaviour of the gas , the equation for ideal gas is
P*V=n*R*T
where
P = absolute pressure
V= volume
T= absolute temperature
n= number of moles of gas
R= ideal gas constant = 8.314 J/mol K
P=n*R*T/V
the work that is done by the gas is calculated through
W=∫pdV= ∫ (n*R*T/V) dV
for an isothermal process T=constant and since the piston is closed vessel also n=constant during the process then denoting 1 and 2 for initial and final state respectively:
W=∫pdV= ∫ (n*R*T/V) dV = n*R*T ∫(1/V) dV = n*R*T * ln (V₂/V₁)
since
P₁=n*R*T/V₁
P₂=n*R*T/V₂
dividing both equations
V₂/V₁ = P₁/P₂
W= n*R*T * ln (V₂/V₁) = n*R*T * ln (P₁/P₂ )
replacing values
P₁=n*R*T/V₁ = 2 moles* 8.314 J/mol K* 300K / 0.1 m3= 49884 Pa
since P₂ = 1 atm = 101325 Pa
W= n*R*T * ln (P₁/P₂ ) = 2 mol * 8.314 J/mol K * 300K * (49884 Pa/101325 Pa) = -3534.94 J
Answer:
Part a)

Part b)
if both sides are rough then it will reach the same height on the other side because the energy is being conserved.
Part c)
Since marble will go to same height when it is rough while when it is smooth then it will go to the height

so on smooth it will go to lower height
Explanation:
As we know by energy conservation the total energy at the bottom of the bowl is given as

here we know that on the left side the ball is rolling due to which it is having rotational and transnational both kinetic energy
now on the right side of the bowl there is no friction
so its rotational kinetic energy will not change and remains the same
so it will have

now we know that


so we have




so the height on the smooth side is given as

Part b)
if both sides are rough then it will reach the same height on the other side because the energy is being conserved.
Part c)
Since marble will go to same height when it is rough while when it is smooth then it will go to the height

so on smooth it will go to lower height
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Answer:

Explanation:
We can use the conservation of momentum. The initial momentum is equal to the final momentum:
x-coordinate

(1)
y-coordinate

(2)
We can divide equations (2) and (1):



I hope it helps you!