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

Answer:

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

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

         $\Delta U = -128 - (-4.17*10^{5})$

        $\Delta U = 417331 \ J$