In a sealed bottle, the temperature is raised from 200 K to 400 K.
What happens to the remaining quantities
Pressure (P)
Volume (V)
Moles (n)
Gas constant (R)
Temperature (T)
(doubles / halves / stays constant)
(doubles / halves / stays constant )
(doubles / halves / stays constant)
(doubles / halves / stays constant )
(doubles / halves / stays constant)
According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Pressure (P): If the temperature is increased while keeping the volume constant, the pressure will increase according to the ideal gas law. Therefore, the pressure will double in this case.
Volume (V): If the temperature is increased while keeping the pressure constant, the volume will also increase according to the ideal gas law. Therefore, the volume will double in this case.
Moles (n): The number of moles does not change when the temperature is increased, as it is independent of temperature. Therefore, the number of moles stays constant.
Gas constant (R): The gas constant is a constant value, and it does not change with temperature or any other variable. Therefore, the gas constant stays constant.
Temperature (T): The temperature is increased from 200 K to 400 K. Therefore, the temperature doubles in this case.
To answer your question, we need to refer to the ideal gas law equation:
PV = nRT
1. Pressure (P): According to the ideal gas law, the pressure of a gas is directly proportional to its temperature. Therefore, when the temperature doubles from 200 K to 400 K, the pressure will also double.
2. Volume (V): The volume of a sealed bottle is assumed to be constant (unless it's a flexible container or subjected to some other condition). So, the volume will stay constant in this case.
3. Moles (n): The number of moles remains constant unless specified otherwise. The number of moles will stay constant in a sealed bottle.
4. Gas constant (R): The gas constant (R) is a constant value for a given gas and does not change based on the conditions of the system. Therefore, it will remain constant.
5. Temperature (T): The temperature is being raised from 200 K to 400 K, so the temperature doubles in this case.
In summary:
- The pressure doubles.
- The volume stays constant.
- The number of moles stays constant.
- The gas constant stays constant.
- The temperature doubles.
To determine what happens to the remaining quantities when the temperature of a sealed bottle is raised from 200 K to 400 K, we need to refer to the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Moles
R = Gas constant
T = Temperature
Let's analyze each quantity one by one:
1. Pressure (P):
According to the ideal gas law equation, if the temperature (T) of a gas sample increases while its volume (V) remains constant, the pressure (P) will also increase. In this case, since the volume is sealed and cannot change, the pressure will double. So, the pressure doubles.
2. Volume (V):
In this scenario, the volume of the sealed bottle remains constant. Hence, the volume will stay the same. Therefore, the volume stays constant.
3. Moles (n):
The number of moles in a gas sample remains unchanged by alterations in temperature, pressure, or volume. Therefore, the moles stay constant.
4. Gas constant (R):
The gas constant (R) in the ideal gas law equation is a constant value that does not change. Thus, the gas constant remains constant.
5. Temperature (T):
In this situation, the temperature of the sealed bottle is raised from 200 K to 400 K. When the temperature increases, the kinetic energy of the gas particles also increases. According to the ideal gas law equation, if the temperature doubles and all other variables remain constant, the volume will also double. Therefore, the temperature doubling will cause the volume to double.
To summarize:
- Pressure doubles.
- Volume stays constant.
- Moles stay constant.
- Gas constant stays constant.
- Temperature doubles the volume.