The pressure on a gas at −43◦C is doubled,
but its volume is held constant. What will the
final temperature be in degrees Celsius?
Answer in units of ◦C
To compute the final temperature, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure and amount of gas are held constant.
Since the volume is held constant, we can rewrite Charles' Law as:
(V₁ / T₁) = (V₂ / T₂)
Where:
V₁ = initial volume
T₁ = initial temperature
V₂ = final volume
T₂ = final temperature
From the information given, the volume is held constant, so V₁ = V₂. Therefore, the equation becomes:
(V / T₁) = (V / T₂)
Since the volume cancels out, we have:
1 / T₁ = 1 / T₂
To find the final temperature (T₂), we need to rearrange the equation:
T₂ = (T₁ / 1) × (1 / 2)
The pressure doubled, so we divide the initial temperature by 2:
T₂ = T₁ / 2
Given that the initial temperature T₁ is -43◦C, we can substitute this value into the equation:
T₂ = (-43 / 2)
Calculating, we find:
T₂ ≈ -21.5◦C
Therefore, the final temperature will be approximately -21.5◦C.
To find the final temperature in degrees Celsius when the pressure of a gas is doubled while keeping its volume constant, we can use Charles's law. Charles's law states that the volume of a gas is directly proportional to its temperature in Kelvin, as long as the pressure and moles of the gas remain constant.
Here are the steps to calculate the final temperature:
1. Convert the initial temperature from degrees Celsius to Kelvin. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature. In this case, the initial temperature is -43°C, so we have:
Initial temperature in Kelvin = -43°C + 273.15 = 230.15 K
2. Since the volume is held constant, we know the initial and final volumes are the same.
3. Use the combined gas law equation, which relates the initial and final temperatures and pressures of a gas, to find the final temperature.
The combined gas law equation is:
(P1 × V1) / T1 = (P2 × V2) / T2
Since the volume is constant, we can simplify the equation to:
P1 / T1 = P2 / T2
Here, P1 is the initial pressure, T1 is the initial temperature in Kelvin, P2 is the final pressure (which is twice the initial pressure), and T2 is the final temperature we want to find.
Plugging in the values, we have:
P1 = Initial pressure
T1 = 230.15 K
P2 = 2P1 (since the pressure is doubled)
T2 = final temperature in Kelvin (which we want to find)
Therefore:
P1 / T1 = P2 / T2
P1 / 230.15 = (2P1) / T2
Cross-multiplying and rearranging the equation:
2P1 × 230.15 = P1 × T2
Now we can solve for T2:
T2 = (2P1 × 230.15) / P1
Simplifying further:
T2 = 460.30
4. Convert the final temperature from Kelvin to degrees Celsius by subtracting 273.15 from the final temperature in Kelvin:
Final temperature in degrees Celsius = 460.30 - 273.15 = 187.15°C
Therefore, the final temperature will be 187.15°C.