What Is the Final Temperature of a Mixture of Oxygen and Air?

[gamx]

Homework Statement

An oxygen supply system mixes oxygen at 105 K and room air at 307 K at equal mass flow rates. What is the temperature of the resulting mixture in K? (c of oxygen = 918 J/kgK, c of air = 1012 J/kgK)

Homework Equations

$$Q=mc\Delta T$$ and $$Q=mL_f$$

The Attempt at a Solution

(105 x 918 + 1012 x 307) / (918 + 1012) = 210 K ( not a single inkling about the validity of the answer ) -_- . The inadequancy of my lecture notes really leaves me clueless =/

 

[Oerg]

firstly, we must define delta T clearly. delta T is the change in temperature of both mixtures, and we can define delta T as the temepreature change from 105K, and then the temperature change for the room air is (307-105)=202K, 202-deltaTK.

Equate both equations together in the first equation you gave and you have the answer.

 

[ogb p]

I would first check the units to ensure that they are consistent. In this case, both specific heats have units of J/kgK, so the units are consistent.

Then, I would use the correct formula for finding the final temperature of a mixture, which is:

T_f = (m_1T_1 + m_2T_2) / (m_1 + m_2)

Where T_f is the final temperature, m_1 and m_2 are the masses of the two substances, and T_1 and T_2 are their respective temperatures.

Plugging in the given values, we get:

T_f = (1/2 x 105 K x 918 J/kgK + 1/2 x 307 K x 1012 J/kgK) / (1/2 x 918 J/kgK + 1/2 x 1012 J/kgK) = 210 K

This confirms that your answer of 210 K is correct. As for the validity of the answer, it is within a reasonable range and makes sense based on the given temperatures. However, it is always good practice to double check calculations and make sure all assumptions are valid.