The rms speed of a sample of gas is increased by 5% .
What is the percent change in the temperature of the gas?
What is the percent change in the pressure of the gas, assuming its volume is held constant?
please help!!
The rms speed of a sample of gas is increased by 8% .
What is the percent change in the temperature of the gas?
What is the percent change in the pressure of the gas, assuming its volume is held constant?
PLEASE HELP
THANKS :)
To find the percent change in temperature and pressure of the gas, we need to understand the relationship between temperature, pressure, and root mean square (rms) speed of gas molecules.
1. Percent change in temperature:
The rms speed of gas molecules is directly proportional to the square root of the temperature. Mathematically, it can be written as:
v ∝ √T
Where:
v = rms speed of gas molecules
T = absolute temperature
To find the percent change in temperature, we can use the approximation:
(∆T/T) ≈ (1/2)(∆v/v)
Where:
∆T = change in temperature
∆v = change in rms speed
T = initial temperature
v = initial rms speed
Therefore, for a 5% increase in the rms speed, (∆v/v) = 0.05, and let's assume the initial temperature and rms speed to be T and v, respectively.
(∆T/T) = (1/2)(0.05)
(∆T/T) = 0.025
∆T = T * 0.025
The percent change in temperature (∆T) can be calculated by dividing the change in temperature (∆T) by the initial temperature (T) and multiplying the result by 100:
Percent change in temperature = (∆T / T) * 100
Percent change in temperature = (T * 0.025 / T) * 100
Percent change in temperature = 0.025 * 100
Percent change in temperature = 2.5%
Therefore, the percent change in the temperature of the gas is 2.5%.
2. Percent change in pressure:
Assuming the volume is held constant, the pressure of an ideal gas is directly proportional to the square of its rms speed. Mathematically, it can be written as:
P ∝ v^2
Where:
P = pressure
v = rms speed of gas molecules
To find the percent change in pressure, we can use the approximation:
(∆P/P) ≈ 2(∆v/v)
Therefore, for a 5% increase in the rms speed, (∆v/v) = 0.05.
(∆P/P) = 2(0.05)
(∆P/P) = 0.1
The percent change in pressure (∆P) can be calculated by dividing the change in pressure (∆P) by the initial pressure (P) and multiplying the result by 100:
Percent change in pressure = (∆P / P) * 100
Percent change in pressure = (0.1) * 100
Percent change in pressure = 10%
Therefore, the percent change in the pressure of the gas, assuming its volume is held constant, is 10%.