Pressure and Temperature -- Quick Concept Check

forestmine

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

pV=nRT

p_1/T_1=p_2/T_2

3. 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.