Calculating pressure change with temperature?

In summary, to calculate pressure change with temperature, the ideal gas law formula PV = nRT can be used, where P represents pressure, V represents volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents temperature. The resulting pressure will be in atmospheres if the units of liters, atmospheres, moles, and Kelvin are used. Temperature and pressure are directly proportional according to the ideal gas law, with the average kinetic energy of gas molecules increasing as temperature increases, resulting in an increase in pressure. However, there is a limit to how much pressure can change with temperature, known as the critical point. Factors such as the number of gas molecules, volume of the container, and type
  • #1
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How do I determine pressure in psi, if I know the temperature. Like I aired my tires up to 80psi at 80F, how would I calculate what the pressure in my tires would be at 90F?
 
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  • #2
With a constant volume: P1/T1=P2/T2. T is absolute temperature, so 80F is actually 80+460=540 R (Rankine scale).
 
  • #3


To determine the pressure in psi at a given temperature, you can use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin.

To calculate the pressure at a different temperature, you can rearrange the equation to solve for pressure: P = nRT/V. Since the number of moles and volume of gas in your tires are likely to remain constant, you can simplify the equation to P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

In your example, we can plug in the values for P1 = 80psi and T1 = 80F (which is equivalent to 26.7 degrees Celsius) and solve for P2 at T2 = 90F (which is equivalent to 32.2 degrees Celsius):

(80psi)/(26.7+273)K = P2/(32.2+273)K

P2 = (80psi)(305K)/(305K+305K) = 160psi

Therefore, if the temperature in your tires increases from 80F to 90F, the pressure will increase from 80psi to 160psi. It is important to note that this calculation assumes that the volume and number of moles of gas in your tires remain constant. Any changes in these factors can affect the accuracy of the calculation.
 

1. How do you calculate pressure change with temperature?

To calculate pressure change with temperature, you can use the ideal gas law formula: PV = nRT. P represents pressure, V represents volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents temperature. Rearranging the formula to solve for pressure (P), we get P = (nRT)/V. This formula can be used to calculate pressure change when temperature changes.

2. What units should be used when calculating pressure change with temperature?

The units used for pressure change with temperature will depend on the units used for the other variables in the formula. The ideal gas constant (R) has a value of 0.0821 L·atm/mol·K when using the units of liters, atmospheres, moles, and Kelvin. Therefore, if these units are used, the resulting pressure will be in atmospheres. Other units such as pascals, torr, or mmHg can also be used as long as they are consistent with the units of the other variables.

3. How does temperature affect pressure?

According to the ideal gas law, pressure and temperature are directly proportional, meaning that as temperature increases, pressure also increases and vice versa. This is because as temperature increases, the average kinetic energy of gas molecules also increases, resulting in more frequent and forceful collisions with the container walls, thus increasing pressure.

4. Is there a limit to how much pressure can change with temperature?

Yes, there is a limit to how much pressure can change with temperature. This limit is known as the critical point, which is the temperature and pressure at which a gas can no longer be condensed into a liquid, no matter how much pressure is applied. Above the critical point, gas and liquid become indistinguishable and are referred to as a supercritical fluid.

5. Are there any factors other than temperature that can affect pressure?

Yes, there are other factors that can affect pressure, such as the number of gas molecules (n), the volume of the container (V), and the type of gas (R). Additionally, external factors such as altitude, gravity, and atmospheric pressure can also have an impact on pressure. These factors must be taken into consideration when calculating pressure change with temperature in real-world situations.

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