Question

The volume of the gas decreases from 500cc to 300cc when a sample of gas is compressed by an average pressure of 0.6 atm. During this process, 10 J of heat is liberated. The change in internal energy is:
A. -2.16J
B. 12.156J
C.2.16J
D.101.3J

Answer 1

Hint: The first law of thermodynamics is also known as the law of conservation of energy. The law states that the energy can neither be created nor be destroyed but can transfer from one system to another. The equation of the first law of thermodynamics gives the relation between the internal energy, heat, and work done.

Complete step by step answer:
Given,
The initial volume of gas is 500 cc.
The final volume of gas is 300 cc.
The external pressure is 0.6 atm.
The heat liberated is 10 J.
As heat is released by the system,
$q = - 10J$
The work done is calculated by the equation as shown below.
\[W = - {P_{ext}}.\Delta V\]……(i)
Where,
W is the work done.
${P_{ext}}$ is the external pressure applied.
\[\Delta V\] is the change in volume.
The change in volume is calculated as shown below.
$\Delta V = {V_2} - {V_1}$
$\Rightarrow \Delta V = 300 - 500$
$\Rightarrow \Delta V = - 200cc$
\[\Rightarrow \Delta V = - 0.2L\]
To calculate the work done, substitute the values in equation (i).
$W = - 0.6 \times ( - 0.2)$
$\Rightarrow W = 0.12L - atm$
\[\Rightarrow W = 12.16J\]
The equation for the first law of thermodynamics is shown below.
$\Delta U = q + W$……(ii)
To calculate the internal energy substitute the value of heat and work in equation (ii).
\[\Delta U = - 10 + 12.16\]
$\Rightarrow \Delta U = 2.16J$
Thus, the value for change in internal energy is 2.16 J.

Therefore, the correct option is C

Note:
Heat and work are only ways by which the energy can move from system to surrounding and vice-versa. The heat and work are not a state function but their sum, that is the change in internal energy is independent of the path therefore it is said to be a state function.