Question

A sample of 4.50 g of methane occupies 12.7 dm3 at 310 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm3. (b) Calculate the work that would be done if the same expansion occurred reversibly.

Answer 1

Answer:

(A) Work done will be 87.992 KJ

(B) Work done will be 167.4 KJ            

Explanation:

We have given mass of methane m = 4.5 gram = 0.0045 kg

Volume occupies $V_1=12.7dm^3=12.7liters$

And volume is increased by $3.3dm^3$ so $V_2=12.7+3.3=16liters$

Temperature T = 310 K

Pressure is given as 200 Torr = 26664.5 Pa

(a) At constant pressure work done is given by

$W=P(V_2-V_1)=26664.5\times (16-12.7)=87992.85J=87.992kj$

(b) At reversible process work done is given by $W=nRTln\frac{V_2}{V_1}$

We have given mass = 4.5 gram

Molar mass of methane = 16

So number of moles $n=\frac{mass\ in\ gram}{mol;ar\ mass}=\frac{4.5}{16}=0.28125$

So work done $W=0.28125\times 8.314\times 310ln\frac{16}{12.7}=167.4J$