Question

When fuel is burned in a cylinder equipped with a piston, the volume expands from 0.255 L to 1.45 L against an external pressure of 1.02 atm. In addition, 875 J is emitted as heat. What is the DE for the burning of the fuel?

Answer 1

Answer : The value of $\Delta E$ for the burning of the fuel is, -998.5 joules.

Explanation :

First we have to calculate the work done.

Formula used :

$w=-p_{ext}dV\\\\w=-p_{ext}(V_2-V_1)$

where,

w = work done  = ?

$p_{ext}$ = external pressure = 1.02 atm

$V_1$ = initial volume of gas = 0.255 L

$V_2$ = final volume of gas = 1.45 L

Now put all the given values in the above formula, we get :

$w=-p_{ext}(V_2-V_1)$

$w=-(1.02atm)\times (1.45-0.255)L$

$w=-1.22L.atm=-1.22\times 101.3J=-123.5J$

conversion used : (1 L.atm = 101.3 J)

Now we have to calculate the change in internal energy of the system.

$\Delta E=q+w$

$\Delta E=-875J+(-123.5J)$

$\Delta E=-998.5J$

Therefore, the value of $\Delta E$ for the burning of the fuel is, -998.5 joules.