Air is filled at 60deg C in a vessel of open mouth. Upto what temperature should the vessel be heated so that one-fourth of the air may escape?
Ans 171degC
PV = n R T
P,V and R are constant
so n T is constant
n1 T1 = n2 T2
n2 = .75 n1
n1 T1 = .75 n1 T2
T2 = T1/.75
T1 = 273 + 60 = 333
so
T2 = 333/.75 = 444
444-273 = 171
thank you soo much :)
thnx
Jagat we cannot use Charles law because the container is open moles at not constant
Can anyone explain it more clearly.......please as soon as possible 😞😞😞
But if we use Charles law such that v1/t1= v2/t2
Then the answer becomes 249.75 K
Ad how the volume is constant.
It is I think volume is changing by 3/4 parts. I'm in dilemma. Can anyone clear my doubt ??
Thats the answer according to S.Chand's also 171K enx for solving
To solve this problem, we need to use the ideal gas law which states that the pressure of an ideal gas is directly proportional to its temperature.
1. First, let's determine the initial and final pressures of the gas. Since the vessel is open, the pressure inside the vessel is the same as the atmospheric pressure.
2. The proportion of the air that escapes tells us that only three-fourths (or 75%) of the initial air will remain inside the vessel. Therefore, the final pressure of the air will be 75% of the initial pressure.
3. Since the gas law also states that the pressure and temperature of an ideal gas are directly proportional, we can say that the final temperature will also be 75% of the initial temperature.
4. Let's convert the initial temperature from degrees Celsius to Kelvin by adding 273.15. Therefore, the initial temperature is (60 + 273.15) K.
5. Now, we need to find the final temperature. We know that the final temperature is 75% of the initial temperature. So, the final temperature is (75/100) times the initial temperature.
6. Substitute the values into the equation:
Final temperature = (75/100) * (60 + 273.15)
= (3/4) * (60 + 273.15)
= (3/4) * 333.15
= 249.86 K
7. Convert the final temperature from Kelvin back to degrees Celsius by subtracting 273.15. Therefore, the final temperature is approximately 171 °C.
Therefore, the vessel should be heated to approximately 171 °C for one-fourth of the air to escape.