Calculating Final Temperature Using Ideal Gas Law | Homework Help

[MastersBound]

Homework Statement

A rigid tank contains 5 kg of an ideal gas at 4 atm and T=40 deg C. Now, a valve is opened and half of the mass of the gas is allowed to escape. If the final pressure in the tank is 1.5 atm, the final temperature in the tank is?

Homework Equations

pV=mRT

The Attempt at a Solution

I know pV=mRT but I don't know how to use this equation for to different states i.e. beginning and end state.

 

[vela]

The equation holds for the two different states, so you have
\begin{align*}
p_i V_i &= m_i R T_i \\
p_f V_f &= m_f R T_f
\end{align*}
What are the quantities you know? What other relationship were you given that relates the quantities?

 

[MastersBound]

That is it. That is the whole problem statement. No specific gas or fluid was given.

 

[vela]

I know. There's enough information to solve the problem. Those questions were meant for you to answer.

 

[DeeNos]

To calculate the final temperature, we can use the ideal gas law equation in combination with the fact that the number of moles of gas remains constant in this process. This means that the initial and final states of the gas are related by the following equation:

p1V1 = p2V2

Where p1 and V1 are the initial pressure and volume, and p2 and V2 are the final pressure and volume. We can also use the fact that the mass of the gas is halved, which means that the final volume is also halved from the initial volume.

So, we can set up the following equation:

p1V1 = p2(0.5V1)

We can rearrange this equation to solve for p2:

p2 = (2p1)

Now, we can substitute this value for p2 into the ideal gas law equation and solve for the final temperature (T2):

p1V1 = (2p1)(0.5V1) = mRT2

T2 = (p1V1)/(2mR)

Substituting in the given values, we get:

T2 = (4 atm)(5 kg)/(2)(0.5)(8.314 J/mol*K) = 239.5 K

Therefore, the final temperature in the tank is 239.5 K or approximately -33.5 degrees Celsius.