Pressure and Temperature - Quick Concept Check

[forestmine]

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!

 

[jedishrfu]

shouldnt T be in Kelvins ie absolute temperature?

 

[forestmine]

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?

 

[smize]

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.

 

[forestmine]

Ok, should have caught that. Thanks guys.