Question

A gas is compressed from an initial volume of 5.35 L to a final volume of 1.23 L by an external pressure of 1.00 atm. During the compression the gas releases 128 J of heat.

Required:
What is the change in internal energy of the gas?

Answer 1

The change in internal energy is
`\Delta U = 417331 \ J`

Step-by-step explanation:

From the question we are told that

The initial volume is
`V_i = 5.35 \ L`

The final volume is
`V_f = 1.23 \ L`

The value of the external pressure is
`P = 1.00 \ atm = 1 * 101325 = 101325 \Pa`

The energy released by the gas is
`Q= -128 \ J`

The negative sign show that energy is released from the system

Generally the workdone on the gas is mathematically represented as

`W = P (V_i - V_f)`

substituting values

`W = 101325 *(1.23 - 5.35)`

`W = - 4.17*10^(5) \ J`

The change in internal energy is mathematically evaluated as

`\Delta U = Q - W`

substituting values

`\Delta U = -128 - (-4.17*10^(5))`

`\Delta U = 417331 \ J`