A vessel of volume V = 30 litre contains an ideal gas at temperature. T = 0°C. Keeping temperature constant, a part of the gas is allowed to escape from the vessel causing the pressure to fall down by ΔP = 0.78 atm. Find the mass of the gas released. Its density under normal conditions is p= 1.3 g/itCorrect answer is '30.4'. Can you explain this answer?

Question

A vessel of volume V = 30 litre contains an ideal gas at temperature. T = 0&deg;C. Keeping temperature constant, a part of the gas is allowed to escape from the vessel causing the pressure to fall down by &Delta;P = 0.78 atm. Find the mass of the gas released. Its density under normal conditions is p= 1.3 g/itCorrect answer is '30.4'. Can you explain this answer?

Answer

Let m and P be the initial mass and pressure of the gas inside the vessel. Therefore,
PV = (m/M) RT ...(1)
where M is the molecular weight of the gas in the vessel.
After a part of the gas is released , we have

...(ii)
where , m is the mass of the remaining gas in the vessel.
Hence, mass of the gas released is equal to (subtracting (2) from (1)

Now, under normal conditions (P₀ = 1 atm. T = 273K), density of the gas is given to be p . Therefore, we find.

or, M / RT = P/ PO
Thus,

Now here V = 30 * 10^-3 m³

and, P_o =1atm.
Therefore,

Answer

A c b

Answer

K. The vessel is placed in a room at a temperature of T = 300 K. Calculate the final pressure of the gas in the vessel if the vessel is perfectly insulated and cannot exchange heat with the surroundings.

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas

Since the vessel is perfectly insulated and cannot exchange heat with the surroundings, the total number of moles of gas in the vessel remains constant. Therefore, we can rewrite the ideal gas law equation as:

P1V1/T1 = P2V2/T2

Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas
V2 = final volume of the gas
T2 = final temperature of the gas

Given:
V1 = 30 liters
T1 = 0 K
T2 = 300 K

Since the vessel is perfectly insulated, the volume of the gas does not change during the process. Therefore, V2 = V1 = 30 liters.

Now we can solve for P2:

P1V1/T1 = P2V2/T2
P1*30/0 = P2*30/300
P2 = P1*T2/T1
P2 = P1*(300 K)/(0 K)
P2 = ∞

Therefore, the final pressure of the gas in the vessel is infinity when the vessel is perfectly insulated and cannot exchange heat with the surroundings.

Similar Physics Doubts

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