Calculate the final centigrade temperature required to change 20 litres of gas at 120°C and 1 atmosphere to 25 litres at 2 atmosphere.
the answer does no correspond
ond with the one on the textbook
What's the answer to the question?
Busola
The answer in the text book is 23 degree celcius and I don't seem to be getting it with ur formula.
Busola
Pls what's the answer?
I don't get it
To solve this problem, we can use Boyle's Law and Charles's Law, which are the gas laws that relate the pressure, volume, and temperature of a gas.
Boyle's Law states that for a fixed amount of gas at a constant temperature, the product of the pressure and volume is constant. In equation form, it is written as:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Charles's Law states that for a fixed amount of gas at a constant pressure, the volume of the gas is directly proportional to its temperature. In equation form, it is written as:
(V1 / T1) = (V2 / T2)
Where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Given:
Initial volume (V1) = 20 liters
Initial temperature (T1) = 120°C
Initial pressure (P1) = 1 atmosphere
Final volume (V2) = 25 liters
Final pressure (P2) = 2 atmospheres
Now, let's find the final temperature (T2):
Step 1: Use Boyle's Law to find the product of pressure and volume for the initial and final states.
P1 * V1 = P2 * V2
(1 atm) * (20 L) = (2 atm) * (25 L)
20 atm * L = 50 atm * L
Step 2: Use Charles's Law to relate the initial and final temperatures to volume.
(V1 / T1) = (V2 / T2)
(20 L / 120°C) = (25 L / T2)
(20 / 120) = (25 / T2)
Step 3: Cross multiply and solve for T2.
20T2 = 120 * 25
20T2 = 3000
T2 = 3000 / 20
T2 = 150°C
Therefore, the final centigrade temperature required to change 20 liters of gas at 120°C and 1 atmosphere to 25 liters at 2 atmospheres is 150°C.
Pls work out the question
Calculate the final centigrade temperature required to change 20 litres of gas at 120°C and 1 atmosphere to 25 litres at 2 atmospheres.
Pressure × Volume / Temperature = Number of molecules
PV / T = N
Convert 120°C to 393.15°K
Original state:
1 atmosphere × 20 Liters / 393.15°K = N moles
Final state:
2 atmosphere × 25 Liters / T°K = N moles (solve for T)
Since N remains constant, we can combine the two statements:
1 × 20 / 393.15 = 2 × 25 / T
Solution:
20 / 393.15 = 50 / T
0.05087116877 = 50 / T
T × 0.05087116877 = 50
T = 50 / 0.05087116877
T = 982.875°K
T = 709.725°C
PV=kT, so PV/T is constant
You want T such that
2*25/(T+273) = 1*20/(120+273)