A cylinder contains a gas with the pressure of 125kpa at a temp. of 200k. What is the temp. of the gas at a pressure of 100kpa?
P1/T1=P2/T2
125kpa/200K=100kpa/T2 in Kelvin.
Solve.
WHy I can't post a question .everytime a try to post a question it said there is an error contact jishka can you help me?
To find the temperature of the gas at a pressure of 100 kPa, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in liters)
n = Number of moles
R = Ideal Gas Constant (8.314 J/(mol*K)).
Given:
P1 = 125 kPa
T1 = 200 K
P2 = 100 kPa (desired pressure)
Step 1: Convert the given temperatures to Kelvin.
T2 = T1 * (P2/P1)
Step 2: Substitute the given values into the equation and solve for T2.
T2 = 200 K * (100 kPa/125 kPa)
T2 ≈ 160 K
So, the temperature of the gas at a pressure of 100 kPa is approximately 160 K.
To determine the temperature of the gas at a pressure of 100 kPa, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in kilopascals, kPa)
V = volume (in liters, L)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in kelvin, K)
In this case, we have the initial pressure P1 = 125 kPa and temperature T1 = 200 K. We want to find the final temperature T2 when the pressure is P2 = 100 kPa.
To solve for T2, we need to keep the other variables constant (volume and number of moles) since we do not have any information about them.
The first step is to rearrange the ideal gas law equation to solve for temperature:
T = PV / (nR)
Now we can calculate the initial temperature T1 in kelvin:
T1 = (125 kPa) * (200 K) / (nR)
Similarly, we can calculate the final temperature T2 in kelvin:
T2 = (100 kPa) * (V) / (nR)
Since the volume and number of moles are constant, we can equate the two expressions for temperature:
(125 kPa) * (200 K) / (nR) = (100 kPa) * (V) / (nR)
Next, we can simplify the equation by canceling out nR on both sides:
125 kPa * 200 K = 100 kPa * T2
Now, we can isolate T2 by dividing both sides of the equation by 100 kPa:
T2 = (125 kPa * 200 K) / 100 kPa
Now let's perform the calculations:
T2 = 25,000 KPa * K / 100 kPa
T2 = 250 K
Therefore, the temperature of the gas at a pressure of 100 kPa is 250 K.