A gas sample has a pressure of 0.997 atm at a temperature of 21.3 °C. If the pressure decreases to 0.865 atm, what is the new temperature in degrees Celsius?
-17.7 °C
18.5 °C
• 66.2 °C
• 255 °C
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure (0.997 atm)
V1 = initial volume (assuming it remains constant, we can omit it)
T1 = initial temperature (21.3 °C + 273.15 = 294.45 K)
P2 = final pressure (0.865 atm)
V2 = final volume (assuming it remains constant, we can omit it)
T2 = final temperature (what we need to find)
Plugging in the values, we can rewrite the equation as:
(0.997 atm * 294.45 K) / (21.3 °C + 273.15 K) = (0.865 atm * T2) / T2
Simplifying:
293.65765 atm*K = 0.865 atm
Solving for T2:
T2 = (0.865 atm * (21.3 °C + 273.15 K)) / 0.997 atm
T2 = 18.524 °C + 273.15 K
T2 = 291.674 K
Converting back to Celsius:
T2 = 291.674 K - 273.15
T2 = 18.524 °C
Therefore, the new temperature is approximately 18.5 °C.
To find the new temperature, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 is the initial pressure
P2 is the final pressure
V1 is the initial volume (which is not provided, but we can assume it is constant since it is not mentioned)
V2 is the final volume (which is not provided, but we can assume it is constant since it is not mentioned)
T1 is the initial temperature
T2 is the final temperature (which is what we want to find)
Given:
P1 = 0.997 atm
T1 = 21.3 °C (which we need to convert to Kelvin since the gas law uses absolute temperature)
First, we convert the initial temperature to Kelvin by adding 273.15 to it:
T1 = 21.3 °C + 273.15 = 294.45 K
Next, we can rearrange the formula and solve for T2:
(P1 * V1) / T1 = (P2 * V2) / T2
Since V1 and V2 are assumed to be constant, we can cancel them out:
P1 / T1 = P2 / T2
Rearranging the formula to solve for T2:
T2 = (P2 * T1) / P1
Substituting the given values:
T2 = (0.865 atm * 294.45 K) / 0.997 atm
Calculating the value:
T2 ≈ 255 K
Finally, converting the temperature from Kelvin back to Celsius by subtracting 273.15:
T2 ≈ 255 K - 273.15 = -18.15 °C
Therefore, the new temperature is approximately -18.15 °C.
To find the new temperature in degrees Celsius, you can use the combined gas law equation. The combined gas law equation relates the pressure, volume, and temperature of a gas sample. It is given by:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures, respectively
V1 and V2 are the initial and final volumes, respectively
T1 and T2 are the initial and final temperatures, respectively
In this case, we are given the initial and final pressures, and we need to find the final temperature.
Let's assign the given values to the variables:
P1 = 0.997 atm
T1 = 21.3 °C
P2 = 0.865 atm
Now, we need to solve for T2. Rearranging the equation, we have:
T2 = (P2 * V2 * T1) / (P1 * V1)
Since no information is provided about the volumes, we can assume that the volume remains constant. Therefore, we can cancel out V1 and V2 from the equation. The equation simplifies to:
T2 = (P2 * T1) / P1
Plugging in the values:
T2 = (0.865 atm * 21.3 °C) / 0.997 atm
Calculating this expression, we find:
T2 ≈ 18.5 °C
Therefore, the new temperature in degrees Celsius after the pressure decreases to 0.865 atm is approximately 18.5 °C.
So, the correct option is: 18.5 °C