a gas is filled in a vessel at 27 degree Celsius. to what temp should it be heated so that it 1/3rd of of the gas escapes out of the vessel?
my attempt to solve;
i tried applying charles law. so, V1/V2= T1/T2.
V2= V1+V1/3= 4V1/3
hence, applying charles law
V1/V2= 3/4
T1/T2= 300/T2
SO SOLVING WE GET T2=400KELVIN.
which is wrong.
ans is 450kelvin.
HELP!
Put
V2 = V1 V1/2
ie. whatever the value of escape gas is given subract 1 digit from its denominator and add to intial volume.
For ex:
escape gas given 1/4 then 4 - 1 = 3 . Add V/3 to intial volume
hey well wisher your soln makes me get right answer but can u please tell why we are doing this ,
To solve this problem, you are on the right track by using Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant. However, there are a few errors in your calculations.
Let's break it down step by step:
1. Start with the initial volume of the gas, V1.
2. According to the problem, 1/3rd of the gas escapes, so the remaining gas would be 2/3rd of the original volume. Thus, the final volume of the gas, V2, would be (2/3)V1.
3. Apply Charles's Law: V1/V2 = T1/T2, where T1 is the initial temperature and T2 is the final temperature.
4. Substitute the values: V1 / ((2/3)V1) = T1 / T2.
5. Simplify the equation: 3/2 = T1 / T2.
6. Cross multiply: 3T2 = 2T1.
7. Solve for T2: T2 = (2/3)T1.
Now, we need to find the temperature at which 1/3rd of the gas escapes, so T2 should be this temperature.
8. Set T2 as the unknown temperature and T1 as the initial temperature (27 degrees Celsius or 300 Kelvin).
9. Substitute the values: T2 = (2/3)(300).
10. Calculate: T2 = 200 Kelvin.
So, according to the calculations above, the temperature at which 1/3rd of the gas escapes is 200 Kelvin, not 450 Kelvin as mentioned in your question.
Therefore, it seems there might be an error in the provided answer. Please double-check the information and ensure that the given answer is accurate.