Question

A gas absorbs 200 J of heat and expands against the external pressure of 1.5 atm from a volume of 0.5 litres to 1.0 litre. Calculate the change in internal energy.
A). 124 J
B). 224 J
C). 114 J
D). 154 J

Answer 1

Hint: For this problem, firstly we have to use the formula to calculate work i.e. \[\text{W = -}{{\text{P}}_{\text{External}}}\triangle \text{V}\] and then we will use the formula of internal energy i.e. $\Delta \text{U = Q + W}$ where, $U$ is the internal energy, $Q$ is the heat and $W$ is the work that is done by the system.

Complete step by step solution:
- In the given question, we have to calculate the change in the internal energy by using the given data and then choose the correct answer.
- In question, it is given that the heat supplied to the system is 200 J. Whereas the initial and final value of the volume is 0.5 litres and 1.0 litres.
- Also, the external pressure that is exerted on the system is 1.5 atm.
- Now, according to the first law of thermodynamics internal energy can be expressed as:
$\Delta \text{U = Q + W}$ …. (1)
- Here, we have to find the value of change in internal energy that is denoted by $\Delta \text{U}$ and we know the value of Q or heat is 200 J.
- But here the value of work done is unknown. So, firstly we will calculate the work by elaborating its formula that:
\[\text{W = -}{{\text{P}}_{\text{External}}}\triangle \text{V}\]
$\text{W = -1}\text{.5 (1 - 0}\text{.5) = -0}\text{.75 L atm or -75}\text{.99 J}$
- Now, by putting all the given values in equation (1) we will get:
$\Delta \text{U = 200 - 75}\text{.99 = 124 J}$

Therefore, option (A) is the correct answer.

Note: The first law of thermodynamics explains the conservation of the energy which means that the energy can be transformed into another form but it cannot be lost or it cannot be created or destroyed.