Question

The latent heat vaporization of water is 2240 J/gm. if the work done in the process of expansion of 1 g is 168 J, then an increase in internal energy is
A. 2408 J
B. 2240 J
C. 2072 J
D. 1904 J

Answer 1

Hint: According to the First Law of Thermodynamics, the universe's energy content remains constant. Energy cannot be generated or destroyed, but it may be changed from one form to another. Mathematically expressed as $\mathrm{\Delta }U=\mathrm{\Delta }Q-\mathrm{\Delta }W$ where W is the work done on or by the system, U is the internal energy and Q is the heat added or removed from the system.

Formula used:
1. $\mathrm{\Delta }Q=\mathrm{\Delta }U+\mathrm{\Delta }W$
Where W is the work done on or by the system, U is the internal energy and Q is the heat added or removed from the system.
2. Q=mL
Where Q is the heat and m is the mass of the object and L is the latent heat of vaporization.

Complete step by step solution:
First let’s discuss the first law of thermodynamics. First Law of Thermodynamics states that the amount of energy in the universe is constant. Energy cannot be generated or destroyed, but it may be changed from one form to another. The law of conservation of energy is another name for this rule.

By using Q=mL and we are given that mass of water is 1g and L is 2240J/gm
Therefore, Q= 2240J

Now here in the question latent heat of vaporization which the heat energy required to turn a liquid into a gas. This heat energy is stored in the liquid's molecular bonds. When these bonds are broken, the heat energy is released and converted into kinetic energy, which causes the liquid to vaporize. So, we can say that it is the amount of heat transferred into the system. Next, look that the gas is expanding means work done by the system. So, we take it with a negative sign. If we put all the given values on the equation then we get.
$\mathrm{\Delta }U=\mathrm{\Delta }Q-\mathrm{\Delta }W$
$\mathrm{\Delta }U=2240-168$
$\mathrm{\Delta }U=2072J$

Hence, the change in internal energy is 2072 J and our correct option is C.

Note: The universe's energy content is constant, according to the First Law of Thermodynamics. It is possible to change the shape of energy, but neither creation nor destruction are possible with it. Its mathematical expression is $\mathrm{\Delta }Q=\mathrm{\Delta }U+\mathrm{\Delta }W$. When heat is transferred to the system then we take it with a positive sign and when work is done by the system then we take it negative. Similarly, we When heat is out from the system then we take it with a negative sign and when work is done on the system then we take it positive.