Yet another pressure/volume/temp question. (no fishes)

[Mo]

Hello all, looking for some expert guidance again please! ill just get straight into it;

The Question
A fixed mass of gas has an initial volume v0 (v subscript 0) and an initial pressure p0 .It is first compressed at a constant temperature of 27C until its volume is reduced to $$1/4$$v0 State the pressure of the gas, in terms of p0, at the end of this process. The temperature of the gas is now increased until its volume returns to v0. Throughout this process, the gas is allowed to expand in such a way that its pressure remain constant.Calculate the final temperature, in C of the gas.


My answer (brace yourself!)

a) Boyle's law states that

$$p . v = c$$ So we can deduce that if the volume were to be reduced to a quarter of its original value, then the pressure will increase four-fold.

i.e 4p0 . $$1/4 v0$$ (4p0 multiplied by one quarter of v0)

b)For this part we know that the pressure = 4p . For the volume to return to its original value, it must be multiplied by 4. (and this is where i get it completely wrong .. well maybe a bit before this!) .so

27 + 273 = 300 K

300 X 4 = 1200.
1200 -273 = 927 C

Now that seems incredibly high to me.Im positive i have gone wrong somewhere.Please enlighten me!

Regards,
Mo

ps: Should i have converted the temperature to kelvins? if not then the answer would be 108 C. i could be using the wrong formula even ..

 

[dextercioby]

Hello all, looking for some expert guidance again please! ill just get straight into it;
The Question
A fixed mass of gas has an initial volume v0 (v subscript 0) and an initial pressure p0 .It is first compressed at a constant temperature of 27C until its volume is reduced to $$1/4$$v0 State the pressure of the gas, in terms of p0, at the end of this process. The temperature of the gas is now increased until its volume returns to v0. Throughout this process, the gas is allowed to expand in such a way that its pressure remain constant.Calculate the final temperature, in C of the gas.My answer (brace yourself!)a) Boyle's law states that$$p . v = c$$ So we can deduce that if the volume were to be reduced to a quarter of its original value, then the pressure will increase four-fold.i.e 4p0 . $$1/4 v0$$ (4p0 multiplied by one quarter of v0))For this part we know that the pressure = 4p . For the volume to return to its original value, it must be multiplied by 4. (and this is where i get it completely wrong .. well maybe a bit before this!) .so27 + 273 = 300 K300 X 4 = 1200.
1200 -273 = 927 CNow that seems incredibly high to me.Im positive i have gone wrong somewhere.Please enlighten me!Regards,
Mo
ps: Should i have converted the temperature to kelvins? if not then the answer would be 108 C. i could be using the wrong formula even ..

If the gas is assumed to be ideal,note IDEAL,then it obeys certain simple laws.On of then states that,if a certain process is isobar,then:
$$(\frac{V}{T})_{1}=(\frac{V}{T})_{2}$$
,which includes the ABSOLUTE TEMPERATURE,MEASURED IN KELVINS.
The tempertures will be 300K the first one,and 1200K the final one.
Again,this is an IDEAL gas,at 1200K,a REAL gas will be partly ionized,and the laws of physics will be different.

Daniel.

 

[Mo]

Thank you for your response.

I gather that this question is talking about ideal gases, since these are the question directly after that chapter.

In an exam situation how would i know though? Would they tell me, or could i say .. "assuming the gas is an ideal gas .." (i doubt they would give me anything that is not an ideal gas since i have not yet learned any formulas for REAL gases .. i don't think ..)

So .. my answers were correct. 1200K ? So in Celsius this is 927 C .

Thanks again for your reply.

Regards,
Mo

 

[dextercioby]

Thank you for your response.

You're welcome!

In an exam situation how would i know though? Would they tell me, or could i say .. "assuming the gas is an ideal gas .." (i doubt they would give me anything that is not an ideal gas since i have not yet learned any formulas for REAL gases .. i don't think ..)

If the problem does not specifically say:"ideal/real gas",then it would be smart to chose the simpler case and simply write on the paper:"Assuming the gas is ideal,then..."

So .. my answers were correct. 1200K ? So in Celsius this is 927 C.Thanks again for your reply.
Regards,
Mo

Yes.Again,u're welcome to post any problems u have.

Daniel.