while the pressure of 1.40 L of a gas is kept constant its temperature increased from 27.0 C to 177 C . calculate the new volume.
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Since PV=kT,
PV/T is constant. So, since P is constant, V/T is constant. That means:
1.4/(27+271) = V/(177+271)
To calculate the new volume, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure is kept constant. The formula for Charles's Law is:
V1 / T1 = V2 / T2
Where:
V1 = initial volume
T1 = initial temperature
V2 = final volume (what we're trying to find)
T2 = final temperature
Let's plug in the given values into the formula:
V1 = 1.40 L (initial volume)
T1 = 27.0 °C + 273.15 (convert to Kelvin) = 300.15 K (initial temperature)
T2 = 177 °C + 273.15 (convert to Kelvin) = 450.15 K (final temperature)
Using the formula, we can rearrange it to solve for V2:
V2 = (V1 * T2) / T1
V2 = (1.40 L * 450.15 K) / 300.15 K
Now let's calculate the value:
V2 = (630.21 L*K) / 300.15 K = 2.099104 L
Therefore, the new volume is approximately 2.10 L.