Understanding the Ideal Gas Law
The behavior of gases can be explained by the Ideal Gas Law, represented as PV = nRT. In this equation:
- P = Pressure
- V = Volume
- n = Number of moles
- R = Ideal gas constant
- T = Temperature in Kelvin
When the pressure is constant, we can simplify the relationship between volume and temperature using Charles's Law, which states that volume is directly proportional to temperature when pressure is held constant.
Initial Conditions
- Initial Temperature (T1): 273 K
- Initial Volume (V1): V
Doubling the Volume
To double the volume (V2 = 2V), we need to find the new temperature (T2) that satisfies the relationship:
- V1/T1 = V2/T2
- Substituting values:
- V/(273 K) = (2V)/T2
Calculating the New Temperature
- Rearranging the equation gives:
- T2 = 2 * 273 K
- T2 = 546 K
Conclusion
To double the volume of a gas at a constant pressure of 273 K, it must be heated to:
- 546 K
This temperature change illustrates the direct relationship between volume and temperature, confirming that increasing the temperature results in an increase in volume when pressure is constant.