Pressure and Temperature - Quick Concept Check

In summary, the conversation discusses the relationship between pressure and temperature in an ideal gas held in a rigid container. The solution is found using the equation pV=nRT and the relation p_1/T_1=p_2/T_2. It is determined that the pressure will be less than 2p when the temperature is increased from 20°C to 40°C. This is because temperature should be measured in Kelvin, as doubling the Celsius temperature also doubles the difference between Kelvin and Celsius. Therefore, it is always important to use Kelvin when working with ideal gases.
  • #1
forestmine
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Pressure and Temperature -- Quick Concept Check

Homework Statement



A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated. At 20°C the gas pressure is p. If we add enough heat to increase the temperature from 20°C to 40°C, the pressure will be less than 2p.

Homework Equations



pV=nRT

p_1/T_1=p_2/T_2

The Attempt at a Solution



Initially I thought the solution was simple. Solving for p_2, we have (p_1*T_2)/T_1. Plugging in 40 for T_2, and 20 for T_1 gives us 2p. Because volume, number of moles, and R are all constant, I thought it just came down to the relation between pressure and temperature, but it turns out the pressure is less than 2p, which I do not understand. Just looking for some clarification...

Thank you!
 
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  • #3


You're right, but I guess I was thinking since 1 celsius degree is equivalent to 1 kelvin, that it shouldn't matter. Essentially, I was thinking if volume is constant, then doubling the temperature should double the pressure, no?

Or does is it significant that we use kelvins, in which case it does turn out to be less than 2p?
 
  • #4


Mathematically, think of Celsius as (kelvin -273)
if you double Celsius, you get (2k - 546) so essentially you double both the difference between Kelvin and Celsius as well as the change in kelvin. You ALWAYS should use Kelvin, It helps.
 
  • #5


Ok, should have caught that. Thanks guys.
 

1. What is the relationship between pressure and temperature?

As temperature increases, the pressure also increases. This is known as Charles's Law, which states that at a constant volume, the pressure of a gas is directly proportional to its temperature.

2. How does pressure affect the boiling point of a substance?

An increase in pressure will increase the boiling point of a substance. This is because higher pressure makes it more difficult for molecules to escape from the liquid, requiring a higher temperature for boiling to occur.

3. Can pressure and temperature both affect the density of a substance?

Yes, both pressure and temperature can affect the density of a substance. As temperature increases, the density decreases, and as pressure increases, the density also increases. This is why substances are less dense at higher altitudes due to lower atmospheric pressure and higher temperatures.

4. How can pressure and temperature be measured?

Pressure can be measured using instruments such as a barometer or manometer, while temperature can be measured using a thermometer. These instruments can be calibrated to give accurate readings of pressure and temperature.

5. What is the ideal gas law and how does it relate to pressure and temperature?

The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This law shows the relationship between pressure, volume, temperature, and the amount of gas present. As temperature increases, the pressure and volume of an ideal gas also increase.

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