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Question: Given that \(1g\) of water in liquid phase has volume \(1c{m^3}\) and in vapour phase \(1671c{m^3}\)...

Given that 1g1g of water in liquid phase has volume 1cm31c{m^3} and in vapour phase 1671cm31671c{m^3} at atmospheric pressure and the latent heat of vaporization of water is 2256J/g2256J/g; the change in the internal energy in Joules for 1g1g of water at 373K373K when it changes from liquid phase to vapour phase at the same temperature is L  L\;:
A) 2256
B) 67
C) 2089
D) 1

Explanation

Solution

Hint
From the first law of thermodynamics we know thatΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta W. Substitute work done asΔW=PΔV\Delta W = P\Delta V. Now put the corresponding values and simplify to calculate the change in internal energy.

Complete step-by-step answer
The first law of thermodynamics is based on the conversion of energy.
According to the first law of thermodynamics, heat given to a system (ΔQ)(\Delta Q) of medium is equal to the sum of increase in its internal energy (ΔU)(\Delta U) and the work done (ΔW)(\Delta W) by the system against the surroundings.
It is given by,
ΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta W
Given:
ΔQ=2256J/g\Delta Q = 2256J/g
P=105PaP = {10^5}Pa
ΔV=1671−1=1670cm3\Delta V = 1671 - 1 = 1670c{m^3}
We know that,
ΔW=PΔV\Delta W = P\Delta V
Substitute the known data in the expression,
2256=ΔU+105×1670×10−62256 = \Delta U + {10^5} \times 1670 \times {10^{ - 6}}
ΔU=2256−167\Delta U = 2256 - 167
ΔU=2089J\Delta U = 2089J
Hence, the change in internal energy is ΔU=2089J\Delta U = 2089J.
The correct option is C.

Note
One can go wrong while writing the first Law of Thermodynamics. In Physics it is ΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta W but in Chemistry it is written as ΔQ=ΔU−ΔW\Delta Q = \Delta U - \Delta W. These differ because of the point of reference. In Physics we are looking at the system from outside. Hence ΔW\Delta W is the work done on the system. While in Chemistry ΔW\Delta W is the work done by the system. Do take care of this distinction in the convention.
Limitation of the first law of thermodynamics is that it does not indicate the direction of heat transfer. It does not tell about the conditions under which heat can be transformed into work and also doesn’t tell why the heat energy cannot be converted into mechanical energy continuously.