Question

A gas is compressed from an initial volume of 5.70 L to a final volume of 1.23 L by an external pressure of 1.00 atm. During the compression the gas releases 120 J of heat. What is the change in internal energy of the gas?

Answer 1

A gas is compressed from an initial volume of 5.70 L to a final volume of 1.23 L by an external pressure of 1.00 atm. During the compression the gas releases 120 J of heat. What is the change in internal energy of the gas?

Solution:

According to the first law of thermodynamics, change in the internal energy of gas is equal to the energy added as heat to the system plus the work done on the system by its surroundings:

$$\Delta U = \Delta Q + \Delta W;$$

We can substitute $\Delta W$ in the equation above by $p\Delta V$, where $p$ -pressure, $\Delta V$ - change of volume, so we get:

$$\Delta U = \Delta Q + p \Delta V;$$

Substituting variables for numbers, we get:

$$\Delta U = -120J + 1.00 * 101325 \text{ Pa} * ((5.7 - 1.23) * 10^{-3} \text{ m}^3) = -120J + 101325 \text{ Pa} * 0.00447 \text{ m}^3 = -120J + 452.92J = 332.92J$$

(We converting pressure to Pascal's for matching units because $[\mathrm{Pa}] = [\mathrm{N} / \mathrm{m}^2]$ and multiplying them by $\mathrm{m}^3$ we get $[\mathrm{N} * \mathrm{m}]$, which is equal to Joules by definition. The Q value was taken with the minus sign, because heat is released by the system).

Answer:

Change in internal energy of the gas is $+332.92\mathrm{J}$

Answer provided by www.AssignmentExpert.com