# Isothermic compression question. Need help

• rigger100472

## Homework Statement

The question I am stuck on is "0.253 m of gas is compressed isothermally from a pressure of 1 bar until its volume is 0.0313 m. Calculate the heat energy transfer. "

## Homework Equations

I understand that work done = Heat transfer because it is isothermal but the equation I have to work with is:

Q=nRT ln V^2/V^1

I don't want the answer to this because I would like to understand, I just don't know what nRT is and how on Earth do I find T if it is not given in the answer.

## The Attempt at a Solution

I have not attempted to answer yet

Last edited:
The question i am stuck on is "0.253m^3 of gas is co

Let's see your attempt at solution.

Sorry about the post being incomplete (don't know what happened). I have now edited the original post.

Hmm this question is bothering me. I definitely used to know how to do it.

I know that in an isothermal compression nRT = P1V1 = P2V2 = constant. Maybe that's how you find T, since you know P1V1 is.

EDIT: I think it is possible that this answer is correct because you're not subbing in a variable PV for NRT, you are subbing in P1V1, which are known, and known to be constant.

The basic idea that you need to understand is

W = $\int^{1}_{2} P dv$

P*V = n*R*T

Here n is the number of moles of the gas, R is the Boltzmann gas constant and T is the temperature. For an isothermal gas of fixed mass, n, R, and T are all constants. Therefore

P = (n*R*T) / V

$\int^{1}_{2} P dv$
= $\int^{1}_{2} (n*R*T) / V dv$
= $(n*R*T)*\int^{1}_{2} 1 / V dv$
= $(n*R*T) * ln (v_{2}/v_{1})$

Although I am not sure how you can find T, you can surely find n*T as you know the volume pressure and R you can use the equation PV = nRT to get n*T. That value you can use in your equation to find your answer

And the relationship PV = nRT comes from the ideal gas relationships which state that

$\frac{P_1*V_1}{T_1} = \frac{P_2*V_2}{T_2}$

As this relationship is true we can say for every mole of gas

$\frac{P_1*V_1}{T_1} = \frac{P_2*V_2}{T_2} = K$

This constant K is the Boltzmann gas constant R, and n is the number of moles of the gas.

Ok thanks for the info guys, I had a go at the question and this is what I came up with. What do you think?

Q=W=nRT∫_(V_2)^(V_1)▒PdV
but nRT=PV
Q=PV∫_(V_2)^(V_1)▒PdV
During isothermal compression
P_1 V_1=P_2 V_2⇒PV is a constant

In this case

PV=0.253

⇒P=PV/V=0.253/V⇒P_2=0.253/V_2 =7.167Bar

⇒Q=PV∫_(V_2)^(V_1)▒〖0.253/V dV〗

⇒Q=PV[0.253lnV]_0.0313^0.253
⇒Q=0.253(0.253ln0.253-0.253ln0.0313)

⇒Q=0.253(0.253ln0.253-0.253ln0.0313)
⇒Q=0.192