A gas sample has a pressure of 0.997 at a temperature of 21.3 the pressure decreases to atm what is the new temperature in degrees Celsius?
To solve this problem, we can use the combined gas law:
P₁V₁/T₁ = P₂V₂/T₂
Where:
P₁ and T₁ are the initial pressure and temperature, respectively.
P₂ is the final pressure.
V₁ and V₂ are the initial and final volumes, respectively.
T₂ is the final temperature.
Given:
P₁ = 0.997 atm
T₁ = 21.3 °C = 21.3 + 273.15 = 294.45 K
P₂ = atm (unknown)
V₁ and V₂ are not specified in the problem, and they are not needed to solve for T₂.
Rearranging the equation to solve for T₂:
T₂ = (P₂ * T₁ * V₁) / (P₁ * V₂)
Since V₁ and V₂ are not specified, we can assume they are equal and cancel them out:
T₂ = (P₂ * T₁) / P₁
Substituting the given values into the equation:
T₂ = (atm * 294.45 K) / 0.997 atm
Simplifying:
T₂ = 295.68 K
Converting back to Celsius:
T₂ = 295.68 K - 273.15 = 22.53 °C
Therefore, the new temperature in degrees Celsius is 22.53 °C.
To determine the new temperature in degrees Celsius when the pressure decreases to atm, we need to use the ideal gas law equation:
PV = nRT,
where:
P is the initial pressure (0.997 atm),
V is the volume of the gas sample (Assuming constant),
n is the number of moles of the gas (Assuming constant),
R is the ideal gas constant,
T is the initial temperature (21.3 degrees Celsius).
We need to first convert the initial temperature from Celsius to Kelvin by adding 273.15:
T (in Kelvin) = 21.3 + 273.15 = 294.45 K.
Next, we set up the equation by letting P1 and T1 represent the initial pressure and temperature, respectively, and P2 and T2 represent the final pressure and temperature, respectively:
P1 * V = n * R * T1,
P2 * V = n * R * T2.
Since the volume (V), number of moles (n), and the ideal gas constant (R) are assumed to be constant, we can simplify the equation as follows:
P1 / T1 = P2 / T2.
Rearranging the equation, we can solve for T2:
T2 = (P2 / P1) * T1.
Since the final pressure is given as atm, P2 = 1 atm. Substituting the values into the equation:
T2 = (1 atm / 0.997 atm) * 294.45 K.
T2 ≈ 295.24 K.
Converting back to degrees Celsius by subtracting 273.15:
T2 ≈ 22.09 degrees Celsius.
Therefore, the new temperature is approximately 22.09 degrees Celsius.
To find the new temperature in degrees Celsius, we can use the combined gas law, which relates the initial and final states of a gas sample. The combined gas law formula is:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure
V₁ = initial volume (assume constant)
T₁ = initial temperature
P₂ = final pressure
V₂ = final volume (assume constant)
T₂ = final temperature
Since we are given the initial and final pressures (0.997 atm and 1 atm) and the initial temperature (21.3°C), we can solve for T₂.
Plugging in the values into the equation:
(0.997 * V₁) / (21.3) = (1 * V₂) / (T₂)
The initial volume and final volume are assumed to be constant, so we can remove them from the equation.
Simplifying the equation:
0.997 / 21.3 = 1 / T₂
Cross-multiplying:
T₂ = (21.3 * 1) / 0.997
T₂ = 21.39°C (rounded to two decimal places)
Therefore, the new temperature is approximately 21.39°C.